As-Salaam-Alaikum. Welcome to lecture number 35 of the course on statistics and probability. Students, you will recall that in the last lecture, I discussed with you various methods of point estimation. You will recall the method of moments, the method of least squares and the very important method of maximum likelihood. After a brief discussion of these methods students, we started the other very important area of estimation and that is interval estimation. You will recall that towards the end of the last lecture, I derived for you the 95 percent confidence interval for mu. You remember that I had told you that generally, we will not do derivations in this course, but I will give you this derivation so that you can realize the lower and the upper limit of the confidence interval. Otherwise, if I would have just given you the formula, it would not have made much sense to you. Students, you will recall that the derivation led us to the formula x bar plus minus 1.96 sigma over square root of n plus and minus meaning that if you minus, you obtain the lower limit and if you plus, you obtain the upper limit. And you will remember that I had told you that in many real life situations, sigma, the standard deviation of the population is not known and then what do we do? The best we can do is to estimate sigma. If we apply the formula summation x minus x bar whole square over n minus 1 then of course, we are talking about small s square which is an unbiased estimator of sigma square. And hence, our formula for the confidence interval now becomes x bar plus minus 1.96 s over square root of n. Let us apply this now to an example. As you now see on the screen, consider a car assembly plant employing something over 25,000 men. In planning its future labour requirements, the management wants an estimate of the number of days lost per man each year due to illness or absenteeism. A random sample of 500 employment records shows the following situation. Now, we have two columns. The first is number of days lost and we have the values none, 1 or 2, 3 or 4, 5 or 6, 7 or 8, 9 to 12 and 13 to 20. And the second column is of the number of employees who had that many absences. 48 persons were not absent even once, 43 were absent either once or twice and 90 either three times or four times. And in this way, we have all the figures in the second column which add to 500 the sample size that we drew. Construct a 95 percent confidence interval for the mean number of days lost per man each year due to illness or absenteeism. Students, you saw that we had a frequency distribution available. But, importantly keep this in mind that this frequency distribution pertains to the sample that we have drawn. As you have seen, there are more than 25,000 employees of that company. But, sample that is of only 500 employees and those records pertain to just 500 people. But, since 500 is a big figure, the absences of the figures have been compiled into a frequency distribution. Our aim is that we do not just want to know for this sample that what is the mean number of absences. In fact, we would like to draw an inference for the whole population. Or if we construct this confidence interval, we can estimate in the form of an interval with which we can attach a level of confidence. So, how do we tackle the situation? So, as you now see on the screen, the computations which are exactly the same as we have learned earlier lead to x bar equal to 5.38 days and s equal to 3.53 days. Substituting these values in the formula, our 95 percent confidence interval for mu comes out to be 5.38 minus 1.96 into 3.53 over the square root of 500. This is the lower limit and for the upper limit, we have exactly the same numbers, the only difference being that the minus sign is replaced by the plus sign. Obviously, we have put the number 500 in the square root sign, because the sample size in this particular problem is 500. And students, upon solving the two expressions we obtain the lower limit as 5.07 days and the upper limit as 5.69 days. Students, aaye is result ko interpret karne ki ek martabha phir koshish karte hain, dekhye level of confidence tha 95 percent. Haam ye kye rahe hain ke agar haam is krisam ke, bohot se confidence intervals construct karte based on the different samples that we could have drawn from this population, to 95 percent of these intervals would have contained the true parameter value. Yani jo true mean number of absences hain haa, wo inme se pachan ve fisad me lai karna tha. Likin of course, ek real life situation mit haam ek hi draw karenge aur ye joh me draw kia uski basis pe jo interval banaa that is 5.07 days to 5.69 days. Ye range kis chees ko represent kar rahi hain, ke haam ye kye rahe hain ke mean number of absences jo hain haa that may be lying in this range and we are saying this on the basis of that procedure in which the level of confidence is 95 percent. Baat zara lambi hogei, likin baat ahem hain. Ek bada hi interesting point aur important point me aapko right now convey kar dena chatiun. Dekhi ye jo derivation last time ki thi uske tahit. The equation that we obtained at the end was that the probability is 0.95 that is 95 percent that x bar minus 1.96 sigma hour square root of n is less than equal to mu is less than equal to x bar plus 1.96 sigma hour square root of n. Ye statement bilkul sehi hai. Jab takke x bar ki value specify nahi hoti, tap tak ye statement sehi hai. Ke is baat ki probability pachan ve feesad hai ke ye jo interval hai that will contain mu. But students, the moment you have actually drawn a sample, actually found in x bar and actually computed limits the way we have just done. Aap agar me is kusam ki statement doon, it is incorrect. Agar me ye statement doon is example me that the probability is 0.95 that 5.07 is less than or equal to mu is less than or equal to 5.69. Yehani mu lies in this range is baat kain kaan pachan ve feesad hai. Mathematically speaking it is wrong. Deke mu jo true population mean hai nahi uski koi ek particular value hai. Ya vo value is interval ke andar hai aur ya vo value is interval ke bahar hai. If it is inside this interval then we should say that the probability of it being in this interval is cent percent that is 1. Ine misal ke tor pe agar aap fars ki je that the true mean is 5.25. To 5.25 to hamesha hamesha aur hamesha 5.07 or 5.69 ke darme anhi lai kare gana, this is cent percent probability. So, in this case we should say that the probability of this happening is 1 aur agar fars ki je that the actual true value of mu is 6.25. So, 6.25 to kabhi kabhi bhi 5.07 or 5.69 ke darme anh lai nahi karshat tana. So, the probability of 6.25 lying in that range is 0. It is neither 1 and nor is it 0.95. Aap ne dekhah ki yeh bahot lambi chauri discussion, main ek mathematical intricacy ke upar kar di, but students this is vitally important. Aap yeh statement nah kabhi dein that the probability that mu is between 5. something and 6. something or whatever, ke a number hain agar aur uske bhi chme mu lai kar rahe hain aur aap kahe ki iss baat ki probability 0.95 hain. Once the sample has be drawn and it has materialized and you have a proper some actual numerical value for x bar and you have correspondingly some actual numerical lower and upper limits, uske baat either that interval contains mu or it does not contain mu. Either the probability of mu lying in that interval is 1 or it is 0. Tuphe sabaal yeh ki sab kuch hum kar kya rahe hain? Main phir repeat karthi hu students ke ham ne yeh kya, ke hamara procedure iss khusam kahe that if we had done this, this process again and again and again, then 95 percent of our intervals of this type would have contained mu. To iss baat pe hum khus hain. Iss baat pe hum khus hain ke hamara yeh process iss type kahe. Aur issi basis pe students, numerous intervals are constructed. Not only for mu, but also for p, the proportion of successes in a binomial population, for sigma square, the variance of any particular population and for other quantities. And in this course as we go along, you will find that I will be constructing intervals for you of this type for mu, mu 1 minus mu 2, p, p 1 minus p 2 and later also for sigma square. And also students for sigma 1 square over sigma 2 square, yani do alag alag population hai, unke alag alag variances. And we are interested ke un variances ka apis me kya relation hai, usko estimate kar na chahate. So, this is a detailed area, a vast area, but yeh jo khus me ne abhi pichle 10 minute ke dharan kaha that is the crux of the matter. Aur issi liye main issko itni detail me explain kya, kyunke from my point of view it is absolutely useless to apply formulas without understanding the concept. Hamesha koshish kijiye ke aap pehle uski, uski rooh tat pachin aur uske baad usko real life situations me appropriately apply kering. Alright, now that we have had a detailed discussion regarding the core concept involved students, let me now bring your attention to another important point. Yeh jo me ne aap ke saath saari discussion pehle bhi ki aur aaj bhi ki, this was pertaining to 95 percent confidence. This is the generally used level of confidence aksar aqad hum yehi use karthe. But this is not the only one that we can use, we can be 99 percent confident, we would like to be more confident why 95 and in some situations we might find that we might be happy with even only 90 percent confidence. To issi liye main, it means that there should be a general formula jis me a saari levels of confidence accommodate hojain. And for that let us now look at the slide that we have. In general the lower and upper limits of the confidence interval for mu are given by x bar plus minus z alpha by 2 s over square root of n where the value of z alpha by 2 depends on how much confidence we want to have in our interval estimate. Ab saawali pehda hota hai ke z alpha by 2 se hammari kya muradhe. If you have a look at the diagram that is now in front of you students, you will find that the two points that we have towards the tails of our standard normal distribution, they are being called z alpha by 2 the one on the right and minus z alpha by 2 the one on the left. Pehlae right side valet point per concentrate ke j this is z alpha by 2 and students the subscript alpha by 2 implies that the area to the right of this particular point is alpha by 2. First ke j hammari z alpha yaha pehla hota to uska matlab yeh hota ke is point ke right side peh joe area hai that is equal to alpha. Acha aap saawali yeh ke yeh hammari yeh jo quantities likhi hui hai one minus alpha alpha by 2 yeh inka kya matlab hai. This sils leh meh the first thing to understand is that the area in the middle of the diagram represents the level of confidence. So, if the level of confidence is 95 percent it means that 1 minus alpha is equal to 0.95 which in turn means that alpha is equal to 0.05 means that alpha is equal to 0.05. Now, when I divide alpha by 2 in other words if I divide 0.05 by 2 obviously I will get 0.025 that is 2.5 percent and this is exactly the area that we would like to have in the right tail as well as the left tail of the distribution. In other words the area on the right as well as on the left is 0.025 and the one in the middle equal to 0.95. So, that when we add all these areas we get 1 the total area under the normal distribution. Generally speaking I repeat in the middle we will have 1 minus alpha which will denote the level of confidence and on the right side as well as on the left side we will have alpha by 2. This Z alpha by 2 here students this Z value we will get from the area table as we have seen before when we were studying the normal distribution in its own right. Whenever you solve a problem of normal distribution then Z value you will get from the area table. Now, as you see on the next slide if 1 minus alpha is equal to 0.95 then the area table gives us the Z value as 1.96, but if the level of confidence is 99 percent then Z alpha by 2 comes out to be 2.575 which can be rounded to say 2.58. Also if the level of confidence is 90 percent then Z alpha by 2 comes out to be 1.644 5 students. I am sure that you should have no problem in finding these values because you have already quite a bit of practice I am sure by now of how to consult the area table of the standard normal distribution. Now, these 3, 4 values I have shared with you actually these you know if you just memorize them then you do not need to read the area table as I have already said 95 percent confidence is the most commonly used level of confidence and for this 1.96 value we get from the area table. So, that can be memorized very easily and the other 2 I have told you that is also very easy to remember. So, you do not have to look at the area table again and again and again 1.645 is the value when we have 90 percent confidence and 2.58 is the value which we will have if we want to have a very high level of confidence and that is 99 percent. Next point is that the formula which we have developed now is X bar plus minus Z alpha by 2 S over square root of n you have seen that I have said S. So, this means that we are assuming that sigma the way the standard deviation of the population is unknown and so we have to replace it by S. This formula this is valid for large n or was central limit theorem be I have to remind you again that if your sample size large so, then your sampling distribution that has mean equal to mu and standard deviation equal to sigma over square root of n, we have derived this interval from that and now finally, we have put S at the place of sigma. Large n is the practical means how large it is means practically how large it is for students. The rule of thumb is that if your n is greater than or equal to 30, then you can apply this formula quite adequately. So, in reality it is only 30 which you can apply. It should have been very large, but we find that even if it is only 30 it is quite adequate. So, as you now see on the slide for large n that is n greater than equal to 30 a sample of this size drawn from an infinite population. The confidence interval for mu is given by X bar plus minus Z alpha by 2 into S over square root of n and S is equal to the square root of sigma X minus X bar whole square over n minus 1. Let us now apply this concept to a few more examples. The Punjab highway department is studying the traffic pattern on the GT road near Lahore. As part of the study the department needs to estimate the average number of vehicles that pass the Ravi bridge each day. A random sample of 64 days gives X bar equal to 5,410 and S is equal to 680. Find the 90 percent confidence interval estimate for mu, the average number of vehicles that pass the Ravi bridge per day. So, let us now look at some of the information available to us. You have seen that sample size is 64 and the rule of thumb given to you is greater than 30. So, we can apply this formula that I have been discussing with you. Next is that X bar is available. We have taken the data of these days. That is, record is kept every day. You know that the tool takes and so on. So, of course, a record is maintained. So, we found that the record of 64 days is X bar is equal to 5,410. On the average, in those 64 days, X bar is equal to 5,410 days. 5,410 vehicles were passing the Ravi bridge each day. On the average, standard deviation a measure of variation. So, that variation the measure is S and as you notice that is equal to 680. So, applying these values in the formula, we obtain 5,410 plus minus z alpha by 2, 680 divided by the square root of 64. Now, since the level of confidence interval that we want to have is 90 percent. Hence, z alpha by 2 is equal to 1.645 and substituting this value, we obtain 5,410 plus minus 1.645 into 680 divided by 8 and solving this expression, the lower limit of our confidence interval is 5,270.2 and the upper limit is 5549.8. Rounding these numbers to the nearest whole number, we obtain 5,270 to 5550. This means that on the basis of 90 percent level of confidence, we are saying that the average number of vehicles that pass the Ravi bridge each day, this average number lies somewhere between 5,270 and 5,550. Here, a very important number is 5,270. So, we are saying that the average number of vehicles that pass this bridge each day, this number lies somewhere between 5,270 and 5,550. No, this is very important. I have said that the average number of vehicles that pass the main number of vehicles lies in this range. I have not said that the minimum number of vehicles that can pass is 5,270. It is possible that the day when only 4000 cars pass, it is possible that the day when 6500 cars pass, it is possible that it is possible that it is possible that it is possible. Let us now have a look at another example. Suppose a car rental firm wants to estimate the average number of kilometers traveled per day by each of its cars rented in a particular city. A random sample of 110 cars rented in this city reveals that the mean travel distance per day is 85.5 kilometers with a standard deviation of 19.3 kilometers. Compute a 99 percent confidence interval to estimate mu. Now, to solve this problem, the first thing to note is that n is equal to 110 much larger than 30 and x bar is equal to 85.5 s equal to 19.3. So, applying these values in the formula, we obtain 85.5 minus z alpha by 2 into 19.3 over square root of 110 for the lower limit and for the upper limit, the minus sign is replaced by the plus sign. Now, since we wish to have 99 percent confidence, therefore, z alpha by 2 is equal to 2.575 and substituting this value, our limits come out to be 80.8 and 90.2. So, we are saying with a very high level of confidence that is 99 percent that the mean distance, travel distance, this mean value lies somewhere between 80.8 or 81 if we round it, 81 kilometers and 90.2 that is 90 kilometers. So, this is the way say students, you have seen that we give a range of values and we say that our parameter lies in this range. We say this with a certain level of confidence. Now, I would like to draw your attention to another very interesting and important way of interpreting a confidence interval. As you now see on the screen, because of the fact that sigma x bar is equal to sigma over square root of n, our confidence interval can be conveniently written as x bar plus minus z alpha by 2 into sigma x bar, where sigma x bar of course, represents the standard error of x bar. The confidence interval for mu can therefore be defined as x bar plus minus a certain number of standard errors of x bar. In other words, we can say that our confidence interval is a point estimate plus minus a few times the standard error of that estimate. Now, the question arises how many times and the answer is that this thing depends on the level of confidence that we wish to have. In the case of 99 percent confidence, the in order to estimate mu our z alpha by 2 is equal to 2.58 which is approximately equal to 2.5 or in other words 2.5. So, we can define our confidence interval as x bar plus minus 2.5 times standard error of x bar. Similarly, in the case of 95 percent confidence z alpha by 2 is equal to 1.96 which is approximately equal to 2. So, in this case we can define our confidence interval as x bar plus minus 2 times the standard error of x bar and so on and so forth. In the case of 99 percent confidence, the standard error of x bar plus minus a certain number of standard errors. In the case of 99 percent confidence, the standard error of x bar plus or 95 percent confidence level chahiye, to those standard errors add or subtract kalli jai. Agar aap usko visualize kare, to it is very simple x bar us mesi agar minus karenge you get the lower limit and agar aap plus karenge you get the upper limit and you get the two limits of your confidence interval. So this is an important and very interesting way of interpreting and remembering the concept of a confidence interval. Or students aap me aapki tavat jo ek bohot hi important point ki tarab dilana chati hu. Aap kahange aaj to sabhi cheezein bohot zyada important hai, well let it be so. Baat hi hai ke aapne dekhah, ke level of confidence is variable aap chahiye to nawe fisad confidence pehi you can be quite happy. But obviously it is intuitively understandable that the higher the level of confidence the better it is. I mean why should it be 90 percent? Why not 99 percent or even 99.99 percent? The problem is that as you raise the level of confidence given any particular sample of a particular size, students your confidence interval widens. Abhi abhi aapne dekhah tha, ke main kaha ke agar pachan ve fisad confidence hai to 1.96 ya 2 standard errors aap piche jayenge, 2 standard errors aage jayenge. So you will get a certain interval, but when you increase the level of confidence to 99 percent aap ku yaad hain aap 2.58 yaani 2.5 standard errors piche jayenge aap 2.5 standard errors aage jayenge and it is a wider interval. So this is the problem, ke agar aap level of confidence ko raise karte hain to aap ka interval widen ho jaata hai to aap kahange ki problem kya hai hone de. No that is not very wonderful students isliye ke the narrower the interval the better. After all aap zara ghor kije aap main statement deine lagi ho zara sochi hai. If I say that I am 99.99999 percent confident that the mean height of the adult males in this particular city, this mean height lies somewhere between 4 feet and 12 feet, will it make any sense? Yaani itna wide interval main dia aur mujhe koi kaini sakta ke ma ghalat kaini hui isliye ke bo mean height vaak hi 4 feet or 12 feet ke dar main hi kaini hogi and I am saying it with 99.99999 percent level of confidence, it does not make much sense. The narrower your interval the better. For example, if I say that I am this much confident that the mean height of these males lies somewhere between 5 feet 6 inches and 5 feet 7 inches students, aap ne dekha immediately aap ka zahan jo hai yeh sko accept karta hai as something to be accepted and to be happy about dekhye kis kadar narrow interval main aapko dia ki bai hi 5 feet 6 inches or 5 feet 7 inches ke dar maian mean height lie karthi. Actually the narrower your interval the better and students what can be the ideal width of your interval, will it not be zero ke bilkul hi koi uski width na ho and you are able to give just one figure. Then you are back to point estimation, the x bar value itself that one lone answer that you have obtained that one single point that is an estimate of your parameter. But as stated in the last lecture the problem with point estimation is that once you have drawn one particular sample and found this point estimate you have no way of saying how close this particular value is to the true parameter value, how close is it or how far is it. agar aap ek interval construct kar leten to uske saath you are able to attach this level of confidence, yani that probability that we have been talking about earlier. aap issari discussion ka jist kya hai hum chahti yeh ke interval narrow bhi ho aur level of confidence bhi hi ho. But students as I just indicated this is not possible for any given particular size in the in because of this reason that as you increase your level of confidence your interval widens iska ilaaj yeh ke aap sample size bada karne because if you look at the formula it is x bar plus minus z alpha by 2 sigma over square root of n jab yeh n uske denominator me aara hai to iska matlab hai ke agar n increase karega to wo puri jo cheese hai which is being added and subtracted from your x bar that entire expression will become smaller obviously as you increase the thing in the denominator that whole thing becomes smaller aur agar aap bo ek choti cheese add or subtract kareenge from your x bar then obviously you are achieving a narrower interval. The problem is that in many situations you cannot afford to increase the sample size beyond a certain value aap ke itne resources nahi hote itne paise aap ke paise available nahi hote budget ke point of view se. Ke jiski bhajase you are able to increase the sample size to as large size that you might wish to have you may have time constraints the smaller your sample the less time you will need to collect the data and to analyze the data and so on and so forth. So, agar aap sample size nahi brhaasakte then you have to strike a compromise between how high a level you wish to have and how wide the interval you can tolerate alright students. Now that we have had a discussion regarding the confidence interval for mu let us proceed to the confidence interval for mu 1 minus mu 2. aap haam ye baat kar rahe ke we have two populations and we are interested in determining the difference between the means of the two populations. Istra ke situation kab arais karegi for example, if there is a boys college and there is a girls college and we are talking about the marks of the students to end munkin hain ke agar vo dono college compete karthe hain to unke jo principles hain unne interest ho is baat me ke determine ki a jai ke dono colleges ke jo marks hain unne kitna fark hain on the average how much is the difference between the marks obtained by the students of the boys college and the marks obtained by the students of the girls college. To aaye is concept ko is apply karthe hain two different examples prior to which of course we first look at the formula for this particular interval. As you now see on the screen the confidence interval for the difference between the means of two populations that is mu 1 minus mu 2 is given by x 1 bar minus x 2 bar plus minus z alpha by 2 into the square root of s 1 square over n 1 plus s 2 square over n 2 and this formula is valid when we are drawing large samples independently from two infinite populations. This formula is being presented in that situation when the population variances sigma 1 square and sigma 2 square are unknown as is generally the case and therefore, we will replace them by their estimates s 1 square and s 2 square. Students ab is course me ek derivation to me kar hi chuki ho regarding confidence intervals. Lekin ab is formulae ki derivation mai nahi karna cha hongi, but I would like to draw your attention to the fact that the basic pattern is exactly the same as before. It is the point estimate plus minus z alpha by 2 into the standard error of that particular point estimate. This situation me jo parameter hon estimate karna chahti hain ya jo quantity hon estimate karna chahti hain that is mu 1 minus mu 2 aur iska jo point estimate hain that is x 1 bar minus x 2 bar aur aapne dekha ke yehi quantity hain jis ke baad hon kar rahe hain plus minus z alpha by 2 into the square root of some big expression. Now, that expression the square root of s 1 square over n 1 plus s 2 square over n 2 this is the standard error or in other words the standard deviation of the sampling distribution of x 1 bar minus x 2 bar our point estimate. Again repeating myself ke asal me to sigma 1 square or sigma 2 square hon hain. Lekin agar wo available nahi hain to hon ne replace kar dete hain by their point estimates. So, let us now apply this formula to an example as you now see on the screen the means and variances of the daily incomes in rupees of two samples of workers are given in the following table the samples being randomly drawn from two different factories. Now, the data is for factory A and factory B the sample sizes are 160 and 220 the mean values are rupees 12.80 and rupees 11.25 and the variances are 64 and 47. Calculate the 90 percent confidence interval for the real difference in the incomes of the workers from the two factories. In order to solve this question the first thing to do is to denote factory A by the subscript 1 and factory B by the subscript 2. Of course, we can reverse this if we want and in that case factory B will be denoted by 1 and factory A by 2, but if we use 1 for A and 2 for B then we find that x 1 bar is equal to 12.80 and x 2 bar is equal to 11.25, n 1 is 160, n 2 is 220 and s 1 square is 64 and s 2 square is 47. Applying all these values in the formula we obtain the lower limit as 0.27 and the upper limit as 2.83. Of course, in this formula we have put z alpha by 2 is equal to 1.645 because we are interested in a 90 percent confidence interval. Students you have seen that our interval is 0.27 and upper limit is 2.83. Now, how we will interpret this? We are saying that on the basis of 90 percent confidence we can say that the difference between the incomes of the workers of factory A and the workers of factory B, the mean difference between their wages lies in this range. On the average, this difference lies in this range. I would like to encourage you to think about this on your own. If you understand that this is a better picture than narrowing, then what you would have to do? You would have had to reduce the level of confidence further. already we are only 90 percent confident. Then we might have had to come down to 80 percent confidence. How foolish it might seem if I were to say that the difference between these two quantities, this difference lies in the range 1.11 and 1.31 and I am saying this with 20 percent confidence. Students, let us apply this very interesting concept to another example. Suppose a study is conducted in a developed country to estimate the difference between middle income shoppers and low income shoppers in terms of the average amount saved on grocery bills per week by using coupons. Random samples of 60 middle income shoppers and 80 low income shoppers are taken and their purchases are monitored for one week. The average amount saved with coupons as well as the sample sizes and sample standard deviations are given in the following table. For the middle income shoppers, we are using the subscript 1 and for the low income shoppers, we use the subscript 2, so that n 1 is 60, x 1 bar is 5.84 dollars and s 1 is 1.41 dollars. Similarly, n 2 is 80, x 2 bar is 2.67 dollars and s 2 is 0.54 dollars. Now, we wish to use this information in order to construct a 98 percent confidence interval to estimate the difference between the mean amounts saved with coupons by the middle income shoppers and the low income shoppers. In order to solve this question, the first thing we do is to compute z alpha by 2 corresponding to level of confidence equal to 98 percent. And if we look at the area table of the standard normal distribution, we find that z alpha by 2 is equal to 2.33 against this particular level of confidence. Substituting all the available values in the formula, we obtain 5.84 minus 2.67 minus 2.33 into the square root of 1.41 square over 60 plus 0.54 square over 80, 2.72 as the lower limit and 3.62 as the upper limit of our confidence interval. In other words, we are saying that on the basis of 98 percent confidence, we estimate that the mean difference in the savings of the two categories of shoppers, this difference lies somewhere between 2.72 dollars and 3.62 dollars. In this situation, students note that we have said 1 middle income shoppers and 2 low income shoppers. So, if we are saying x 1 bar minus x 2 bar and after that our interval is coming like you just saw. So, this means that on the average, middle income shoppers are saving a lot of money as compared with the low income shoppers. If our interval minus something to minus something comes, then we say that low income shoppers are saving a lot of money as compared with the middle income shoppers. See, this is a very simple thing that you subtract from which and after that your answer is positive or negative. According to that, you will interpret that situation and that answer. Students, in today's lecture, we have discussed in considerable detail the concept and the method of constructing confidence intervals. I discussed with you the confidence intervals for mu and mu 1 minus mu 2. In the next lecture, we will be talking about confidence intervals for p and p 1 minus p 2. Until next time, best of luck and Allah Hafiz.


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Brown Dark City entered the territory on west, there's just one way to handle the killers in the spoilers, and that's with the US Marshal and the smell of gun smoke. Gun smoke, starring William Conrad, the story of the violence that moved west with young America, the story of a man who moved with it, Matt Dillon, United States Marshal. Could I give you some more coffee? Uh, yeah, I guess so. How about you, Chester? Yes, sir. Why don't you just leave the coffee pot here on the table, Miss Keller? Well, I sure thing, Marshal. All right. Well, I got some fresh eggs this morning. If you're interested, they were just brought in. Well, good. Good. Cook us up about a half a dozen, huh? Have them for you right away, Mr. Dillon. Fresh eggs. My... I swear, if Del Monaco isn't getting to be about as fancy as some of them in Kansas City, rest your... Well, that's civilization, Chester. Progress. Another five years in Dodge City will be tame, curried, and bridal. I can't believe it, Mr. Dillon. Well, you'll see it. Both of us will see it. That is, if we live that long. Yeah. I beg your pardon, gentlemen. Uh... You Mr. Dillon, the Marshal here? Oh, yes, that's right. Well, I'm sorry to bother you at breakfast, Marshal. My name is Hunter. Ed Hunter. Mr. Hunter. I'm a Deputy Sheriff from Richmond, Virginia. Come in on the side of me this morning. I see. Well, why don't you pull up a chair, Mr. Hunter? All right, thank you, sir. Uh, Chester Proudfoot. Mr. Hunter. How do you do? Here's my first trip to the frontier. I've found it a rather remarkable experience. I can imagine. I want you to have some coffee. I know, thank you. Marshal, I'm here to arrest two men who are wanted with Virginia. No? Here are the warrants and the orders of extradition. I stopped off for them in Topeka. Uh-huh. John Allison. Calvin Moore. Both wanted for murder, huh? Do you know these men, Mr. Hunter? No, sir, I don't. Well, their names aren't familiar to me. I never heard of them. Have you, Chester? No, sir, Mr. Allen. Well, I have some information that may help. Not much on Allison, I'm afraid. He shot and killed a bank teller at Greenbryer last spring. Oh? He's about 30 years old, dark hair and mustache, medium build, an excellent horseman and a confirmed gambler. Well, that's fine. That narrows it down to about two-thirds of the men in Dodge City. Well, possibly I can do a bit better in regard to Calvin Moore, Mr. Dill. Now, he came down to Richmond from the north and set up practices of medical doctrine. He was about 29 at the time. And he ambushed and shot young Roger Boregaard and then left town. That was, uh, 17 years ago. Boregaard's been trying to trace him ever since. Well, I'm afraid that's a pretty long time. Well, I have a picture of Moore, photograph. Well? Of course, he was much younger than this. Well, sometimes there's still quite a resemblance, even after 17. Something familiar about that picture, Mr. Dill? Uh, 17 years. He must be somewhere past 45 now, huh? Hmm. Are you sure that these men are here in Dodge, Mr. Hunter? Reasonably so. Is there something about that photograph that makes you, well, it's too blurred to tell much about it besides he'd be 17 years older now. Yeah, that's true. Uh, I'll tell you what, Mr. Hunter, suppose you leave the picture in the description below with me and I'll check around town and I'll keep in touch with you. Oh, thank you, son. Oh, I wonder if you might suggest a good hotel. Uh, certainly. Why don't you try the Dodge House, it's a corner of Railroad Avenue at the end of the Plaza of the East End. Uh, tell the deacon I sent you. I thank you again, Mr. Dillon. Not the grateful for any help you can give me in this matter. Yeah, sure. So long. You want to see the photograph, Chester? Yes, sir, I do. Well, for Mr. Dillon, that is... Yeah. What are you going to do, Mr. Dillon? I don't know, Chester. He's my friend. I never asked him anything about his life before he came here. It didn't seem to matter. But now the law says he's a murderer. I'm part of the law. So now it does matter. Maybe it's not him. No, it's him all right, Chester. You saw it the same as I did. It's dark. Work, work, work, work. This is the first chance I've had this week to clean a few instruments properly. Gunshot wounds. Oh, man. I'll lay odds. I'm the only doctor in the United States who makes three-fourths of his living off of gunshot wounds. That's a rough country, Doc. Yes, indeed it's a rough country. Maybe you ought to have stayed back east. See, broken bones, babies, and gunshot wounds. Well, I wouldn't know the first thing about a good civilized case of gout anymore. Uh, what part of the east did you come from, Doc? See, I went to medical school in Boston. I studied consumption, colic, liver complaints. Never had a case of liver complaint in all the time I've been here, though. No, I guess that kind of thing is more common down soft around Richmond, Virginia, for instance, huh? Stop beating around the bush. You've got something on your mind, and it's bothering you. Look, Doc, a deputy sheriff from Virginia came in on the morning train. He's got a warrant for murder against a man named Calvin Moore. He's got a photograph of Moore taken 17 years ago. Would you like to look at it? All things are taken from us and become portions and parcels of the dreadful past. Are you Calvin Moore? It wasn't murder, Matt. They said it was murder, of course. The Beauregardes were an important family. Would you like to tell me about it? Oh, not much to tell, Matt. I had been in practice in Richmond about a year. It was a girl. Beautiful girl. The spirit and fire and that soft radiance that only southern girls seem to have. Yeah, it was so long ago. I bet I know South myself now. Roger Beauregard and I were both caught in this girl. He was a typical Virginia gentleman, hot-headed. He used to have in his own way. He started threatening me, warning me. And I laughed it off. Then one day I was coming back from a case and I ran into Roger on a country road. He had a pair of dueling pistols, and he challenged me. What? Well, that's not a crime, Doc. That's self-defense. It's not a crime here, anyway. Well, I tried to talk him out of it, but he was crazy mad. He shoved one of the pistols in my hand and he pulled back on his horse and he leveled his gun. I had no choice. We both fired. He missed. I didn't. Self-defense? Yes, but there were no witnesses and I was an outsider, a Yankee. So you ran for it, is that it? I ran for it. St. Louis, Virginia City, Montana Territory, the Panhandle, Wichita, Abilene, and Dodge. I changed my name to Charles Adams. And the, uh, the girl, Doc. What happened to her? I waited for her in St. Louis. We were married there. Two months later, she died of typhoid fever. Hell, you never know. No matter how much you figure you understand somebody, you just quite never know. I can't go back there, Matt. I've got no defense. Why, I mean prisoner. I brought in prisoner. I won't go back now. Not, Doc. Look, Hunter is here after two prisoners. I've got no right to, to my own rules to go after one man and keep the other one covered. I always figured that the only kind of law that would work out here's an honest law. What are you gonna do? Doc, I don't know. You're late, Matt.  Is Chester around here? Yeah, over there by the Feral Table. Matt, what about this Virginian who's been hanging around for the last two days? Oh, Hunter, he's a deputy sheriff. Got a couple of warrants to serve. Why? Well, he's been asking questions. Some of the boys are getting a little skittish. Now, there's no call for it, as long as they're not named Allison or Moore.  What's it look like? I figured maybe it was just killing time. Hi, Marshall. Bunko? I bought you a drink, Kitty. It's over on a bar. All right. Thanks. Matt, I'll be off in a couple of hours. Drop her off. Yeah. Yeah, maybe. I understand you've got a rival lawman in town, Marshall. Well, there's a deputy here from Virginia, if that's what you mean. I always figured you were the law here. Is he short, Miss Tom Marshall? Say the word, we'll run him out. I ever ask you for help, Bunko? Well, no. When a man's short and dodged, I'll run him out. And no offense, Marshall. You keep your own sense tight. Don't worry about anybody else, huh? I'll see you, Bunko. I swear I never saw anybody such bad-looking all my life. My gracious, he ought to swear off their own stickless dud. Oh, Chester. Hmm? The old Jethro Keener. He just lost three weeks' pay.  Well, so that's why he's feeling big. Um, come on, Chester, let's take a walk. Yes, sir. Three weeks' pay. Mercy, I never saw such luck. What about Doc, Chester? He turned in a couple hours ago. That's when I came on over here. How's he acting? About as usual. No signs of planning to run out, if that's what you mean, Mr. Gunn. One thing he's doing, though, that he's never done before, he's toting the gun. Good evening, Marshall. Oh, hello, Mr. Hunter. Since you didn't come to me, Mr. Dillon, I've come to you. I'm wondering what progress you've made. Well, I, uh, I'm still checking. Any results at all, Marshall? Well, I don't have much to go on, you know. Now Calvin Moore was a doctor by profession. He might still be practicing. I suggest we investigate the local doctors. Well, that wouldn't take long. We've only got one, Doc Adams. How long is he been here? About four years. How old a man is he? Late 40s, I imagine. But he doesn't show much resemblance to the photograph you gave me. Well, maybe you're too used to him to notice the resemblance. Yeah, maybe. I'd like to look him over myself. Well, uh, he's pretty busy out on calls most of the time, and not all the time. No, not all the time. All right, Mr. Hunter, I'll bring him around. Mr. Dillon? Yeah, he should have answered by now. What time, Chester? He's gone. Well, now, he might have got called out on the case. Yeah, I know, but I don't... Hey, what? That was across the plaza, down toward the Dodge House. Come on, Chester. Sure is sturdy enough to smoke. That's across the street, edge of the railroad yards, I think. That you, Marshal? Yeah. What happened, Mr. Hunter? Somebody tried to kill me. I started into the hotel. They fired from the dock here. I fired back, but he got away. Get a good look at him? Oh, no, I just saw the flashes. Now, this is an easy time to get killed in, Mr. Hunter. So it seems. About that doctor, Marshal, you didn't bring him around. Well, uh, he's out on call. I think I want to meet him more than ever now. He will return for the second act of gun smoke in just a moment, but first, there's a world of wonderful entertainment awaiting you every weekday and the daytime, with CBS Radio's roster of wonderful dramatic serials. This Monday, listen in. And now, for the second act of gun smoke. What time is it, Chester? 2.15 a.m., Mr. Dillon. I sure hope we don't have spend the whole night waiting here. I don't see how Doc puts up with the smell of all this medicine. He's used to it, I guess. I suppose a man can get used to anything except dying. You think it could have been him that fired those shots, Mr. Dillon? Chester. There's somebody coming. Come on in, Bunko. Doc's not here, but he'll probably be... Well, what happened to your arm? I... I got thrown into a barbed wire fence. Here, let's have a look at it. No, no, no, no, it's all right. The gunshot wound all right. All right, both of you! Is that the same gun you tried to kill Hunter with, Bunko? Stay where you are, Marshal. Yeah. Around 30 years old, dark hair, moustache, medium build, excellent horseman, confirmed gambler. Wanted from John Allison. Alias Bunko Benson. Am I right, Bunko? He's not taking me back there.   Put away the gun. Stay back. I'm warning you, Bunko!  All right, Chester, let's get him over to the jail. Just hold still now, Bunko. Just one more second. And I'll have hold that bullet now, and then we'll just... Ah! Now, add that one to your collection, Matt. Don't make Hunter a present of it. It wasn't bad shooting to be firing in the dark at a gun flesh. He'll never get me back to Virginia. Now, hold still, Bunko. I don't expect a man to tie a bandage with his arm waving around like a mare's tail in fly time. See, how'd you know he'd come to my office, man? I didn't, Doc. We were waiting for you. There we are. Now, that ought to stop the bleeding. And don't loosen it up any more. And you live the hang yet. Don't worry about my hanging, Doc. I'll outlive you. Well, in view of the circumstances, I'd say the odds are about even. Well, Matt, shall we adjourn to the front office? Yeah, come on, Doc. Lock the cell, will you, Chester? Well, I turned in at 10 o'clock tonight. I got one hour of sleep. They called me over to Mrs. B. Hands. She thought her baby was on her way. False alarm, of course, usually is the first time. And I got back, and I came straight over here. Uh, Doc, you were wearing a gun earlier today. What'd you do with it? Oh, I put it back in the drawer where it belonged.  Was that where you were waiting in my office?  Look, Doc, I've tried to think of some way out of this. A way out for both of us. I got one man under arrest back there now, and I can't rightly set myself up as a judge and free the other man. I'd even hoped you'd cut and run for it. You'd get away if you did, you know. Hunter doesn't know the country. I've been running for 17 years, Matt, and it's still caught up with me. I'm too old to ruin any father. What are you gonna do? I'm a lawman, Doc, right or wrong. I guess I'm under arrest. No, I didn't say that. I just said that... Is Doc Adams here? There's a... Oh, well, there you are, Doc. Yes, yes, what's the trouble? The fellow over in the railroad yard's asleep on the track who's drunk, I guess. They were switching cars. You better come, Doc. He's awful bad. Mr. Dillon, that ought to be enough. Good, Chester, you're ready, Doc. Are you ready as I ever do? All right, let's go. Uh, he said near the loading pins down this way, I guess. Yes, sir. Looks like some lights over there. People around here. Marshall, is that you? Yeah, yeah. Oh, Hunter, I thought you went to bed hours ago. I'm a light sleeper, Mr. Dillon. I heard there's an accident over in the yards. Thought it might give me a chance to meet your local doctor. Well, I guess you can meet him right now if you want to. Doc, this is Ed Hunter, Doc Adams. How do you do, sir? Mr. Handy? I got one of your prisoners locked up, Mr. Hunter. John Allison. Known here as Bunko Benson. Good.  He caught one of your bullets in his arm. Oh, I see. Why, then, it's one down and one to go. There's Calvin Moore. Dr. Calvin Moore. This is no time to stand around making Chen music. I'm sorry, Hunter. Well, that's quite all right, Marshall. I'll go with you. Will you pardon us, please? All right, will you move back? Well, here, please. Here, Doc, this way. Yeah, I'm right where you're at. All right. Please stand back now, will you? Give Doc a chance to work. Yes. Please, if you please, just stand back. Oh, bad is right. Well, we'll do what we can. Come on. That man who's hurt, Marshall, who is he? I'm just a drifter. I've been around Dodge a couple of years. He calls himself Texas Joe. No friends or family. He knows where he came from. It's the usual story. I'll use you now, Tex. We'll have you fixed up here in just a couple of shakes. Is that you, Doc? That's right. I told him, get you. Be all right if you got here. Why, sure. Be all right. You just lie still now. Yeah. Certainly has to work under primitive conditions. Doc? Yeah. Chester, will you get those lanterns going and give Doc some more life? Yes, Mr. Mayor. Yeah, he's the only real doctor this side of Abilene. Really? Is there anything I can do to help? I guess not, Miss Kelly. Thanks anyway. Poor old Tex. Why, he stopped in the restaurant not more than four hours ago. I fixed him a meal. Well, you never know. Well, Doc can pull him through if anybody can. Sure he can. Put one of those lanterns on the other side there, Chester. Yes, you got it. You seem to have a lot of faith in this Dr. Adams. They've got reason to, Mr. Hunter. Matt, could you give me a hand here? Oh, yeah. Yeah, sure, Doc. Lift his head up just a little bit there, Matt. All right. Not much of a chance, all right. What I can do is make him comfortable. Marshall, Dylan. No, don't try to talk, Tex. You're going to be all right. You, you've been decent to me, Marshall. Just a bum, but you treated me square. You and Doc, only friends I got. Sure, Tex. I, I got one more favor to ask. Could someone, could someone read me some scripture? Well, Tex, I, I just don't recall anything. Marshall, I, I know something. Mrs. Kelly, I, I doubt a few things. I, I can hear. Please. Lord is my shepherd. I shall not want. He maketh me lie down in green pastures. He leadeth me beside the still waters. Mrs. Kelly. He restores my soul. Mrs. Kelly. I, I think that's enough. Well, can't win them all, I guess. No, you can't win them all, Doc. Well, I, I, Doctor, as the only physician here, I suppose you also function as coroner. That's right. This man will be buried in the name of Texas Joe. Eh, don't you worry about that. Boothill is full of men buried under nicknames. Let me go. In this country we... Doc, Doc, I just can't remember. Oh. What, Kitty? Oh, Doc, I've been sitting up with Mrs. Bay, and you're left too soon. She needs you over there, right away. Well, then it wasn't a fault to learn. No. All right, Kitty, I'll be there just as quick as I can, but... Well, as soon as I... Kitty, you go on back over and do what you can for her, huh? Doc will be along. All right, Matt. You'd better hurry. Well, Mr. Hunter, I, uh... Our gentleman, this seems to have been my lucky night. Both my fugitives located within an hour of each other. I guess there's nothing I can do to... One of them safely in jail, and one of them dead. What? I didn't you notice the resemblance, Marshall? That Texas Joe there. He's obviously the man in the photograph I saw it immediately. Well, Mr. Hunter... I hope you'll take all the necessary steps to see that he's buried under his real name, Calvin Moore. His death, of course, closes the case, and I'll be leaving for Virginia with my other prisoner tomorrow. Well, Mr. Hunter, I... I just don't know what to say. Now, I'd say it's no time to stand around making chin music, Dr. Adams. You have a patient waiting in this town seems to depend on you. Well, of course, but... You've got work to do, Doc. And, uh, Doc, make sure it's a boy. Well, I'll, uh... I'll do my don this, Matt. Yeah. Well, good night, gentlemen. Good night, Doc. Under the direction of Norman McDonnell, stars William Conrad as Matt Dillon, U.S. Marshall. Tonight's story was specially written for Gunsmoke by Les Crutchfield, with music composed and conducted by Rex Corey. Featured in the cast were Lawrence Dobkin, Lou Krugman, Paul Dubov, and Vivi Janis. Parley Bear is Chester, Howard McNeer is Doc, and Georgia Ellis is Kitty. Gunsmoke is heard by our troops overseas through the facilities of the Armed Forces Radio Service. Join us again next week as Matt Dillon, U.S. Marshall, fights to bring law and order out of the wild violence of the West in Gunsmoke. This evening, listen for Lionel Barrymore, your host on CBS Radio Sunday Night Playhouse. There'll be another specially selected historical drama or a classic from literature with a cast of stars perfectly suited for the roles in the story. Every Sunday evening, hear Lionel Barrymore on your Sunday Night Playhouse over most of these same CBS radio stations. Truly an outstanding dramatic experience here at the stars address. Roy Rowan speaking, and remember, for thrilling dramas of escape, listen every Sunday night to the CBS Radio Network.


So, I love the Book of Mormon. The Book of Mormon has made all the difference in the world in my life. For every goal that I've set, for every thing that I've wanted to accomplish, or achievement I've wanted to accomplish, the Book of Mormon has helped me along the way. I think that the most important aspect of the Book of Mormon, besides it being another testament of witness of Jesus Christ, is that life has difficulty in trials and the Book of Mormon can give us very specific help in those trials. And a scripture in the Book of Mormon that I love that helps with that is in Ether chapter 12 verse 6, that says, Wherefore, I, Meron, I would speak somewhat concerning these things. I would show unto the world that faith is things which are hoped for and not seen. Wherefore, dispute not, because ye see not, for ye receive no witness until after the trial of your faith. And that scripture really speaks to my heart, because I think that in most times in life where there's been difficulties, I can't really understand why they happen, or can't really see what I'm supposed to do. But I know as the Book of Mormonist taught me that if I will just have faith in the Lord Jesus Christ that all things will work out for the best, then Book of Mormonist taught me that God is taking specifically care of me and knows me. I know that the Book of Mormon is true and I love that book.


Colombia is a leader in terms of addressing the migration challenges and first and foremost is the fact that rather than turning away the millions of migrants who have come from Venezuela, they've offered them a chance at status in the country, access to health care, access to education and frankly a future here in Colombia and that's really a model for other governments to follow. A partnership between the national government and the local government and IOM to bring health care to migrants and this is important because it's not just the migrants who benefit, it's also the hosting community. An IOM in partnership with a number of other colleagues are ensuring that migrants can get their COVID vaccines, that their children can get their regular vaccines, that women who are expecting babies can get maternal health care. Every person regardless of their migration status has access to health care and access to the COVID vaccine. That's how we keep each other safe but it's also a basic right. So this investment early on, the investment in migrant communities is how we ultimately make communities more healthy, more safe and we really create a more coherent strategy. So to me this is an essential piece of the work that we're doing here.


What's up everybody, Jason here for jaspyscasebrakes.com. 2022 Pinini Prison football just sold out. This is a six box hobby half case break, Patriots number one, all card ship guys, highly anticipated release, finally releasing with the 2022 draft class, which I think is still pretty solid guys. All right, Ramin got the Panthers via filler last spot mojo. Do they really Frank? Yeah, that's something that I would leverage. I don't think I'd ever even do that. I think everybody only really talks about is like Florida and Texas. All right guys, so six boxes in the left, six boxes in the right. Let's see which one we're gonna use here for this side. Roll a one, two, three goes for the left side, four, five, six for the right side. Here we go, roll. That's a four. One, two, three, four, five, six. So we're gonna use this one here for number two. Damn dinks out. How about Mexico guys? Team Mexico right now, up three, one over Canada, which is a crucial game. Canada, USA and Mexico are all two in one, so I think the winner of this game for sure advances. And then it's all up to seeing if maybe USA were to lose to Columbia. And then I think it would go by like tiebreaker.  Yeah, I mean, I'm just a homer for California, but I'd probably live in New York too, probably right. I think I'd choose like LA. I'd choose the Bay Area of North.  That is the question Tristan, we were talking about that earlier. We feel like, I personally feel like Ecuador makes sense in Chicago. You know, obviously Montgomery not there no more. You can get a nice big paycheck there. Good weapon to Justin Fields. They got the money. Well, it depends, James. I think just like everywhere in a big city, I'm sure certain areas are cheaper than others in the suburbs around LA. So, you know, let's say here in Hermosa Beach, super expensive. I mean, you can find like a one-bedroom, one-bath for like maybe 17, 1800, but it's probably really small. Like four hundred square feet or less, honestly. I used to live in Gardena. I was paying, I think like the 1900 for a one-bedroom, one-bath apartment, which was really nice though. I mean, compared to what was out there, you could probably get a decent apartment for probably 15, 1600 dollars. But it's probably closer to 2000, honestly. Just very expensive if you really think about it. But obviously it just depends on how you like to live if you, nice Marriota. David Bell, nice RPA to start us off already. Depends on how nice you like it or not. You know, the nicer, the more expensive it is. I moved to Long Beach, downtown Long Beach, like a year and a half ago, and I love it where we live. I'm paying a little bit more, but you get more amenities and stuff like that, you know. Whoa, card's a little bent there. Hopefully that flattens in a top loader. That's a little Prism Drake London. That looks, I don't know, I don't know if that's in a flat, is that one of those Prism throwbacks? Looks like it. Kyler Murray, that one pack was really, really bent, or warped, I should say. Top load that now to kind of try to start flattening that. I don't think all the packs are like that. I just think it was specifically this one. Really, really warped. Not a good sign for the first box. Hopefully they're not all like that. Wow, what the hell, dude? Dude, this card is literally stuck. It's stuck. Look at this. So sad, dude. Jameson Williams. Sorry about that, Frank. I mean, kind of had to pull it off a part. Well, I hope all the Prisms are not like that, and it's just really this box. Maybe this box was just a little defected or something. Javon Holland, who's a stud as well, to 175. I don't think they're all like this, guys. I think literally something happened with these packs here, and it just got really messed up. I do believe. I don't think they're all like that, because it was just that one stack. Now it's kind of going back to normal. Yeah, but this is a little bit worse than the Vin Baller, honestly. Out of 49, of course, Adam Vinitieri's fine. There you go, there's our second auto. That's for the Indianapolis Colts. Jay Kirby with that one. And Stefan Diggs, 299. We have DeVondre Campbell to 225. Brilliance, that's a cool little insert there. And a Jamal Williams. Where does Jamal Williams go, guys? I feel like he's kind of the odd man out now, right? Out of 249. Type 1 Thornton, actually using Pinini presses. I didn't read that till now. Pinini does sound good, though. New recruits, Desmond Ritter, and a Rashad Bateman. Silver Paddingma Homes. Let's steal that out for you, Gabe. Trey Hendrickson. And look at that. Beautiful Malik Willis, little color maps. Blue Ice, 94 out of 99. It's pretty sweet. I thought Josh Jacobs got a franchise tag, James. And he didn't have an exclusives. I don't think he has a choice. I think he has to either sign it or hold out for a contract with the Raiders. Yeah, I'm interested to see where Miles Sanders goes now. I mean, who knows? I don't know, could this happen? Maybe Miles thinks he's worth a lot more and then his agent and then try to find a suitor and nobody wants to pay them. And then maybe he does come back for really less money, but I don't think so. I feel like some of them are gonna sign him for a decent contract. I just kind of want to know where he's going so that way either I dump his cards now or I hold onto them during the season for early pre-season. The whole Walmart Jackson thing is kind of weird, but I really think it's not that people don't think he's worthy of the contract. I just think that not only do you have to pay the man what he is worth and what he wants, but to give up two first round picks and have to pay the guy, that's kind of tough right there. I think that's the only reason why I think some teams kind of backed up on the Walmart Jackson. This box looks fine, so maybe it was just that weird box. Speaking of the Walmart, this is the fireworks there. Mark Hooper, it's a 75. And I'm a little Garrett Wilson Silver rookie autograph. Couple room with the Jets, Jets, Jets. It's funny that Miles Sanders and Josh Jacobs obviously were running backs in 2019 that actually had a really good season. Is there a final year of their contract? Jamal Williams. Also two guys, I'm gonna be chasing some McNabb autos and colors in here, so if anybody hits one of those, I'm a potential buyer, okay? Breece Hall, it's $1.99. Yeah, I don't know, yeah, it's, I don't know, it's a weird situation with the Walmart Jackson and the Ravens. I feel like they might've got turned off. I feel like obviously he felt like he was worth more than that, although three years, 133 guaranteed, that's, I don't know, it sounds like a pretty good deal to me. But I think the one thing, honestly, is that the Browns contract with Deshaun Watson changed the game forever. It's very unrealistic for other 31 teams. I think the Browns is just totally messed up. They really were desperate. Obviously drafting quarterbacks hasn't been the best thing for them, so they decided to pay this guy everything. And I mean, I don't blame the Walmart Jackson thing, even if that guy's getting paid that much. Have you not seen what I've done in my first X amount of years? I just think he has to realize that that's kind of unrealistic.  Remondria Stevenson, you got a snake's getting him. It's the fondigs. Sorry, I had to quickly take that. But yeah, I don't think so either, Tristan. I hope for Browns country, Browns nation. He does do well for them because they spent a lot on that dude and they're kind of forced to pay that dude no matter what. But yeah, it's kind of hard for me to see them really thinking that he's gonna take them to the promised land. So I don't know, we'll see. Cooper Cup. Yeah, I mean, look, when Calibri signed that contract, after that one year they had, going to the playoffs in the year he had, Clint Portis, that's pretty nice, green scope. I think he was worth it. I really did believe in the guy. Obviously regressed, had a major knee surgery, so it's gonna be kind of tough to come back. But I think Calibri is capable of, man. I just think he needs to kind of grow up, become that leader that I know he can be. But, you know, obviously now it's not looking too good. But, what is this? That's just a silver. Quinn Nelson. I mean, I think people need to realize that Tristan, that there's not many Mahomes. How many Mahomes is there every generation, you know? There's only so many you can find. And even Mahomes is kind of special in that sense. Jake Ferguson, to 225. But you know, I will say, I will say, I think one quarter by that has a lot of potential. You guys can laugh at me, but I think one quarter by that has a lot of potential to be a very big dual threat. Big time is just in fields, honestly. That dude has a cannon, and in college, he wasn't really known for running as much as he did. But now in the NFL, people know how good he can run. He just needs to kind of take that Jalen Hurts step, that leap, you know? Just get better accuracy, and just really better decision-making, honestly. If he can get better at that, obviously get a better team surrounding him, which he is this year, that dude could be legit. And obviously staying healthy is gonna be one thing. Kind of limit those blows. So, look, Jalen Hurts, I think, got there because he obviously devoted all of himself to getting better. Look, Jalen Hurts will never have the arm that all these other guys, all these other guys have. Jalen Hurts' arm is not strong at all. But he doesn't need to have a strong arm, right? I mean, as long as he's making better decisions like he did last year, you know, tucking it, running it, trying to obviously be smart with the football, I mean, as long as he gets time in the pocket, he can make every throw. So, you're not gonna see Jalen Hurts completing a 60-yard, 70-yard bomb all on himself, you know? You're probably gonna see him throwing a 40-50-yard bomb, and then Razir doing the rest. Fadarian Mathis, Joe Mixon, Devin McCordy, Dachshund Hill. Yeah, I think an O-line is clutch, man. Like I said, I think now that you're moving towards running back, you don't gotta pay them much. You know, you can find running backs in later rounds and just pay some of these free agent guys on one-year, two-year deals to kind of get the job done. That saves a lot of money on offense, is that right? I think you do have to pay for a big-time ride receiver, maybe two, to obviously kind of help out your quarterback a little bit, but I think that extra money that you were having to pay for the linemen or for the running back is now what you really wanna beef up and pay that extra second tackle or guard, you know, to a good contract, because yeah, I think it's kind of proven if the quarterback gets more time in the pocket to throw the ball, Christian McCaffrey, I think more successful, right?  But nowadays, obviously, I think the NFL loves those dual threat quarterbacks that obviously can run the ball and get out of the pocket, which obviously helps your case out. You kind of have a pain manning or a tom Brady back there anymore in this league. I think that era is kind of done with. You need to have a little bit of mobility. You know, maybe like a Rogers or Justin Herbert, those guys that can kind of still run and move the ball around, my homes, but if you have a guy like Hurts or fields that can really get out of the pocket and run around, obviously benefits you a lot. Marquis Colston, sensational signature. And we have a little camel, Josh Allen, to 25. 11 out of 25. Whoa, the hype looks cool. That's a purple power, number to 49. And Jordan Davis to 60. Gary Wilson, Mark Ganges. We also do have a top load list for a handful of players. So if I skip like a big time player, don't worry. I'm sure it's gonna get sleeved at least or top loaded. I think our sleeve and top load list is, let me check. Yeah, we're in top load with quite a few players. Malik, Purdy, Kenny Fakis, Amhal, Wilson, Hutchinson, Crystal Lave. That dude has to only be making like $600,000, right? I mean, if Kenny Gainwell is drafted in the third round, he's making a million dollars. I'm gonna have to assume that a seventh round dude is probably making less. But I'd assume Kansas City is probably fairly cheap to live in, cost of living, is it, is it, is it fairly cheap? So I'd assume he'd be fine, right? I think we kind of forget that like in most of the world, most of the United States, like if you're not in LA and New York, you know, some of the bigger cities, like your ren or mortgage is probably like a thousand bucks, or less. So if you're making $500, $600,000, you're doing pretty well. Torrey Holt to $199. St. Clawn Barclay, we got Tyler Higby to $225.  Tristan, there you go, man, out of $99. There we have a Logan Hall for the bucks. Chris Godwin to $225. The Danian Tomlinson, $60. Plejinson, ooh, nice McNabb right there. That's a cool color, Matt Smith, $19 out of $25. And Trayvon Diggs, that's a little vet out of there for the Cowboys. Ed with that one. Rashon Gary to $149. Can you pick it? Terrence Marshall Jr., Troy Anderson. And Devondre Camp. This event so much is exactly what we have seen in the last several days. Surely you find the race for a world that is such a real appreciation for being together in that event. You just feel that, you feel that gratitude and joy. And I tell you what, the stories that we have, they're good to tell of the journeys of each player, whether it's Great Britain, or Mexico, or Canada. This is an extraordinary privilege. Yeah, it is. This is a great spot for this event. The others, you have, obviously, are in Mexico. We're in this, and others, they're obviously in Mexico, they're in close proximity, they really support, hey, just like, Vancho the North, Vancho the North, what else is it?  Two one-pitches in the air, little shallow right, easy, just there. Andrew Howard says, they've done well, but they've gone on it, left off. And they ordered, coming up, and we shut it down, and it has to go, so it's worth getting to go to bed. The state lines will replace, or put it shortly, and recalibrate, or grant safety systems, so automatic emergency braking, and let the majority worry, or poverty. All right, next box. Jonathan Greenard to 75. Travis Etienne to 149. You got David Montgomery to 125. Zaire Alexander to 249. A nice cave on Tibbadoe. I will say, though, the centering in this prison history looks pretty nice, actually. To 125, not to say every single part is centered, but it's pretty good. Derek Henry, purple ice to 225. Denzel Ward to 99. Kenny Pickett to a toggle by low to 199. Tyler Boyd to 175. I feel like, have we got an autograph yet here? Come on, where did the autograph say? Here's one. Dante Cole Pepper to 149, sensational signatures. Little Harvey. Prism brake, that looks awesome. Little Drake London to 99. And a Carson Strong for the Eagles. Did we only get one auto here on this side? Dante Cole Pepper was the only auto, right? Wow, we got dudes. Only one. Hopefully, there's an extra one line in here. Dude, I don't know, dude. I don't even think I've seen Patek, but I've only seen Skye Moore. All right, here we go. Last box. There's Chris Jones. Little Aaron Rodgers. And Damien Harris. There's a Purdy. Whoa, we got a stained glass. There we go, Garrett Wilson. How about that, Adam Kuperman? You know, Adam, I tend to hit you some pretty good jets hits, I will say. And a little Drake London. Great pack right there. Little Mack Dye Jones. And a rookie flashback, Desmond Ritter. With a cave on tip of the toe. 225, there's Brian Cook. You might actually have a paycheck on here, Gilo. I might've just might've passed it up. I feel like in that six boxes, gotta be at least one rookie of most teams. There's Aiden. George Kittle. A Homes fireworks. There's DJ Moore. A lot of color here for the Panthers, which was part of the filler team roundup. And Desmond Ritter. Nice rookie autograph. Kenny Pickett. Aaron Donald. For the Falcons. Jack Lambert. And I have a little smoke on the Joe Borough. Brilliant. I don't think I'll ever say his name ever again differently. And a little boy there. And there you go, guys. That was it. That was the break. Like I said, I might've passed up some base rookies, but don't worry, the top of the list that we have, we will still even top load it. Autograph wise, though. Nice Desmond Ritter. We did get a stained glass. Dante Kohlpepper. Trayvon Diggs. Tori Holtz. Marquis Colston. Clint Portis. Garrett Wilson. Malik Willis there. Obviously we have a ton, ton of color. That whole stack right there. Adam and Terry, Jameson Williams. David Belth. Pat Giotto. And of course, like I said, lots and lots of colors in here for a lot of these teams. So I appreciate it, guys. This is number one. Number two's coming up next, jaspyscasebreaks.com.


Are your thoughts always galloping around? Do you ever wish your mind could reign in those horses? There are decisions in life that require extensive deliberation and thought, such as moving to a different country or accepting a life-changing job. Despite this line of logic, everyone has suffered bouts of overthinking. The only difference is that some eventually come up with a decision, while chronic overthinkers are plagued with questions and doubt. You rehash previous conversations, relive past events, and imagine catastrophic outcomes.  This is debilitating in more ways than one. Not only does it exhaust you mentally and produce anxiety, along with many other health issues, but it also prevents you from moving forward. So here are 10 ways to stop overthinking. 1. Become aware Is running a negative mental commentary second nature to you? If so, it's a habit that you might not be aware of. So the first step to tackling overthinking is to become aware of it. Grounding yourself in your body is a great way to gain awareness.  Other techniques are touching an item and really feeling its material weight and temperature, and putting your hands in water. Becoming self-aware is the first step to changing your mind. 2. Focus on productive problem-solving Do you get wrapped up in the possibilities of what could happen? Do you busy yourself with solutions for a problem you have not yet encountered, or perhaps might not encounter? This type of thought pattern is an example of unproductive thinking. Some examples of unproductive thinking are, if I do this, then this, usually something negative, will happen. Or why does this always happen to me? Unproductive thinking usually starts with fear. Hence, it transforms into a loop of negative thoughts that serve to instill doubt. When something goes wrong instead of wondering why, ask how. Asking how shifts your focus on what can be done now and helps you be more productive. It changes your perspective and helps you focus on what can be done. 3. Schedules of self-reflection time Sitting in a stew of your own problems is not productive. It is time-consuming and never yields positive results. However, making time to reflect can help you see and think about things from a different perspective. It affords you time to assess pitfalls in your plans and how you can do better. It also serves as a mental boundary. If something goes wrong, your instinct may be to run through and see where you failed. However, having a set time to go through and assess what went wrong prevents you from making hasty decisions. 4.  The more you tell yourself not to do something, the more you might find yourself doing it. The same goes for overthinking.  It certainly can be a scary place sometimes. By distracting yourself with, for example, a hobby or exercise, it'll not only make you feel happy doing something you enjoy, but it will put a stop to that stream of negative thoughts. 5.  Whenever you find yourself overthinking about something, ask yourself this. Will it matter 5 years from now? Will it matter a month from now? The chances are that it won't. Life is always changing. Asking yourself such questions helps put things into perspective and gives you a new approach. 6.  When you spend most of the time racing in your brain, it leaves you feeling less aware. Your surroundings take a back seat when your thoughts ride shotgun. Achieving mindfulness does not occur overnight. It requires practice. There are many books, apps and courses and other resources that can help you become more mindful. Practicing mindfulness is a great way to ground yourself in the present. You will be fully attending to what's happening, to what you're doing, to the space you're moving through. By practicing mindfulness over time, you will notice that you overthink a bit less. 7. Do away with perfectionism Perfectionism can be a sign of lingering fears, and it often leads to overthinking. You become perceptive of your actions and how others might perceive them. Perfectionism narrows the scope of your actions, your thoughts and your future. It renders you unproductive and incapable of moving past your problems or failures. When you find yourself wanting to be perfect and start to overthink things, remind yourself that done is better than perfect. 8. Accept your best Are you always pushing yourself to cover that extra mile? Do you ever give yourself a break? Practicing compassion helps you move past your mistakes and let go. When you become attuned to your emotions and they're accompanying physiological cues, you can spot when you need to take a break. By acknowledging your feelings that arise during that moment and saying positive affirmations, you can encourage compassion for yourself. 9. Be grateful Gratitude helps you gain perspective. Sometimes, many problems are not as terrible as they seem. Gratitude opens possibilities for acceptance as well as growth. It can also prevent you from falling into a pattern of negative thinking. 10. Acknowledge your success Picture this, you find yourself amid an overthinking barrage. So what do you do? During that avalanche, remember to take a moment to write down on a piece of paper five things that went well. For example, you cleaned your apartment or stuck to your budget. The accomplishments on your list do not need to be grand, but looking at this list will make you realize that you've succeeded, even in the small things, more than you have failed. When necessary, refer back to this list to keep your thoughts from spiraling out of control. When life gets hectic and overwhelming, it's important to take a step back and breathe. Take a break from the constant information and racing thoughts and, if necessary, ask for help. We hope we were able to give you some insight into some ways that you can stop overthinking. Do any of these describe your experiences? Or did any of the points describe you? Leave a comment down below about your encounters with them, if you'd like. Please feel free to share any thoughts you have as well. If you found this video helpful, be sure to hit the like button and share it with those out there constantly overthinking. Don't forget to subscribe to Psych2Go and hit the notification bell for more new videos. Thanks so much for watching.


So, basically I would like to thank Pathak Sir for giving us this opportunity to develop such a project and we learned a lot in this project about developing and work ethic and working in a team. So, I would like to introduce my team mates Pooja, Archana, then Sonu, Prathmesh, Sudhanshu, Prathik and Prashant. So, our project was basically to get a product design, optical assembly design in order to scan. So, our project was basically to design a fingerprint optical assembly. What currently is being done using the Aakash tablet is that they are using an Aakash tablet for Adhar authentication purpose. They are taking a fingerprint and using that fingerprint they are able to tell the if the person whose fingerprint is there, his other ID matches with that or not. So, what they currently are using they are connecting an OTG cable, with that they are connecting a frutronic tech device, they are connecting that device to that Aakash table and then scanning the fingerprint using that device. What we have done in this project is we have designed our own optical assembly, modified some softwares and created developed some softwares and then we are scanning this fingerprint on our own soft optical assembly and we are using this optical assembly for this authentication purpose. The previous assembly was costing something like 4000 rupees. Our current assembly is on an approximate cost of 180 rupees but with some more modification I think it will be a little more costly than it is currently present. So, I would like Sudhanshu to continue. Hello, I am Sudhanshu Verma from NIT, Nagpur and I was working on the optical assembly of this project. So, the optical assembly we have just we are using the Aakash tablets camera itself to capture the image for authentication of Aadhaar card users. So, this is our optical assembly, our optical assembly consists of 3 parts, the first part is the clamp. So, clamp just is used for making the optical assembly stable on the tablet this way and it also there is a support for the spacer, our spacer is 2 mega definite distance between the fingerprint impression and the camera of the Aakash tablet. So, we have used a spacer for that thing, third part is the optical part, third part is the optical part in which we have used acrylic and on the sides of the acrylic we have used LEDs. So, LEDs, so LEDs we have just put LEDs on the sides of the acrylic such that it illuminates the acrylic perfectly by the concept of total internal reflection and we have used components like black acrylic, black acrylic to cover the whole set of such that no outside light interferes with our fingerprint impression and transparent sheet of acrylic for getting the fingerprint impression and we have used LEDs and given up a 4.5 volt power source to these LEDs and next is the FTIR principle, how we are getting the difference between the edges and values of our fingers. So, FTIR principles in works in such a way that the whole of the acrylic is illuminated due to total internal reflection. So, FTIR principle is frustrated total internal reflection in which the light travels due to total internal reflection reflection it travels in the whole of the acrylic. So, wherever there is just touch the acrylic it the light gets absorbed and hence we are able to get RGB image there RGB there and the parts where values are there they are little bit up than this acrylic. So, they are in the air so they get scattered due to which we get a white part white pass there. So, this is it and now Pooja will continue. Hello everyone I am Pooja Dev from NIT, Nagpur. So, after the image is captured it goes through a series of processing initially as my friend Siddhanchu explained the image gets captured after it is captured it is grayscale what grayscaling does is the RGB image that gets converted into a gray image after that the image gets cropped so that the background is removed and only the fingerprint gets processed after that the image is resized to get a clearer image. So, resizing adaptive histogram equalization is done in adaptive histogram equalization the contrast is spread out so that the clarity of the image is increased after that sharpening is done image sharpening basically brings out the ridges in the fingerprint. So, after sharpening thresholding is done right now you have a grayscaled image that gets turned into a binarized image a binarized image is an image which is white pixels and black pixels after that thinning is done so that the thick ridges those get converted into a pixel thickness and finally, the enhanced binarized image that is sent over to the server for authentication. So, this is the basic workflow and live finger detection this is one technique that basically detects if the finger is of a live person or it is a spoof. So, the fingerprint scanner that can be pulled by using a gelatin fingerprint or a silicon fingerprint. So, what it can be this problem can be solved by using hardware or software. So, right now my friend Prathamesh he implemented the live finger detection. So, he used a software approach basically it makes use of poor detection and perspiration where when you place the fingerprint on the scanner due to perspiration the grayscale of the image changes and this change in grayscale determines whether the finger is of a live person or not, but unfortunately it requires a very high resolution camera and the camera of Akash is providing to be a bit of a problem so, we have been unable to implement it in our model. So, I will tell Archana to continue. My name is Archana and I am going to be talking about the next step in our algorithm. So, first what we do is adaptive histogram equalization. So, in this step what you do is you increase the contrast of the image. Now, by doing this you can easily differentiate between the ridges and the values more clearly. So, what is done is you take the histogram of the image and you spread out the values such that the high intensity values are made even higher and the lower ones are made even lower.  After that you calculate the CDF which is the cumulative density function and then you find that of the histogram and that is the transformation function which is used to transform the input pixels to the output pixels and this is the image that we took from the Akash tablet and before we apply the contrast before the contrast is increased that is the image. But you can see that the histogram is not very equalized and it has peaks. So, what we do is we stretch out the histogram so that the contrast increases. And after we do histogram equalization what we do is we do image thresholding. So, thresholding is used to convert a grayscale image into a black and white binary image. So, in this so the algorithm that we followed is also the algorithm. So, in this first what you do is you once again you make the histogram and you can find out the probabilities of each intensity level. After that for each to find the threshold value you take each value each intensity and you find its weight its mean its variance and within class variance and whichever threshold whichever intensity value gives you the minimum within class variance that is chosen to be the threshold value. So, we when we applied Otsu's algorithm before thresholding this was our grayscale image and you can see that the values on the histogram vary on the grayscale and after applying thresholding we get a binarized black and white image with the values only pure black and pure white. Sonu's going to explain the next. Good afternoon everybody. I will be talking about image sharpening. So, when we sharpen an image what happens is we enhance the details of the image. So, details of the image that was not visible to the eye before they become clear after you sharpen the image. So, like features like the hair strands or the facial features they become much clearer. Now, when you sharpen a fingerprint what happens is the ridges they become more clearer. So, you can identify the ridges in the fingerprint. So, the algorithm that we use is we have used Laplacian kernel based convolution. Laplacian kernel is a standard matrix that is used for sharpening. So, first we take the input image and then we apply the convolution to it and then we get the sharpened image. So, over here we can see before sharpening the ridges are in very clear in the fingerprint but after sharpening you can easily identify the ridges and also in the histogram we can see that after sharpening histogram is a little more distributed that is like more pixels are given more importance and more pixels you show the details of more pixels. Next I will talk about image thinning. In image thinning what we do is we reduce the thickness of the image that is by reducing the number of pixels in the image. Now, this is done because a thinned image it occupies lesser amount of memory and it is also easier to process a thinned image because it contains only very few pixels. Now when we thin the fingerprint what we do is we reduce the thickness of the ridges to one pixel thickness. Now this is done because it is easier to extract details like minutiae points from a thinned ridge and these minutiae points are used for fingerprint recognition and matching etc. So, in the picture we can see this is the original input image and after thinning we get a one pixel thickness ridges. Now I will call Pooja to talk about the future scope. Firstly the optical assembly it can be enhanced by using infrared LEDs or assembly LEDs. Secondly, various techniques like use of polarizing filters and macro lenses can be used to obtain a better image of the fingerprint. Apart from that the problem we faced was that we could not send the image to the server because we did not have access so authentication using the enhanced image could not be done. So, that can be implemented in future. So, the problems we faced during the making of this assembly were firstly finding the distance at which the image is focused and is clear for that the viewing angle of the camera was calculated and the focal length was calculated by doing various experiments. The second problem we faced was initially we were planning to use a glass sheet for capturing the image. However, glass sheet has a green tint which affect that the quality of the image. For that we replaced glass by an acrylic sheet. The third was illumination in an acrylic sheet, the light it was not being distributed properly. To solve this problem a number of LEDs were used and the number of LEDs being used they were varied and finally an optimum number 4 was calculated. The fourth problem we faced was deciding the workflow of the image enhancement process. As I explained earlier the image goes through a number of processing algorithms. So, to solve this problem we first made use of SyLab using different permutations we decided which process gives the most optimum result and finally the process as shown was decided and fifth was implementing it on Aakash tablet. For that we used OpenCV, OpenCV is an open source software and it has a dedicated platform for Android. So, we developed the code using OpenCV and then finally implemented it on Aakash tablet. So, the things we learned in this project were basically image processing using OpenCV. Secondly, we learned using SyLab. SyLab as I mentioned earlier is also an open source software. Then it was the first time we were studying image processing and we studied several algorithms to do the same. The fourth thing we learned Android application development. Creating a hardware assembly we faced as I explained before certain problems were faced and we learned to overcome them and finally we learned how to document a project. Like we made the SRS, the SDD and the project report. So, yeah and apart from the project we had a side project. So, some of some Android applications were made. This is an Aakash dictionary. This is an application that provides formulas and in algebra and geometry. The third is this gives history of India. Then the fourth was plotting graphs. The fifth was incredible India. It gives information about various states in India. The sixth is periodic table. It gives information about the various elements. The seventh is consumer protection. The various rules for consumer protection. The eighth is salt analysis. So, on a concluding note I would like to thank Fatak sir for providing us with this wonderful opportunity to work on Aadhar authentication. I would also like to thank Karman Aages sir for guiding us throughout the process. I would like to thank Prakash sir and Nare sir for helping us build the optical assembly. And I would also like to thank our mentors who guided us through all sticky spots and last but not the least I would like to thank all my team members for contributing so much to the project. And finally we would like to show a demonstration of our application. The first image is the standard image of finger that we took from 3mm pixel camera. It clearly shows the better result than the image we are going to took from this VJ camera. We have to just scan. We have to show the demo. This is the result by the VJ camera on Aakash tablet. We have developed using the different techniques using thinning, thresholding. One question is have you actually tried this application against the Aadhar server? No sir. Why? But I had specifically said where is Rajesh? Who are the mentors? They had a problem actually. The idea was that even if they get a rejection the fact that end to end application is built can be proven only after you connect to Aadhar. So why was that not done? They had approached and they could not get the links properly. Sir we were not able to contact the guy who was there at testing server. In the affordable solutions lab? Anybody from ASL here? Sir we met Rajesh sir but he was not able to contact. Sir because we had to open up the test server to get the data. But the person who had opened it up earlier for testing he wasn't available. Oh at the other end? Yeah at the other end. So we went over the cross section directly. We tried finding different links that we wanted to access. Because even if this camera didn't work you have made the same application run on any other Android tablet right? And you have tested that there you get much better clarity. Now do you have a suggestion on the specification of the camera resolution? Camera resolution is important but what is more important is that the finger should be focused on. Focused upon? Focused upon. So in that for doing that we had ordered some lenses but by the time they arrived it was too late for us to implement. The lenses? Yes we have ordered some lenses. So whom have you transferred this technology so that the work can be continued further? What we have mentioned in the reports for the further? The report is with the person here who has read your report. If he has not read it now it's unlikely that he will read it over the next two months. What about your software engineers? So will that person be able to carry this forward? I had personally promised Nandan that we will make sure that it will work. They are currently using it as I said using an external device. We are very keen to use it. I wanted a more clearer recommendation from you regarding both the focal requirement as well as the camera resolution. So let me ask the question other way round. Are you sure that using those additional lenses that have not been obtained the present resolution of the Akash camera will be adequate? If I think it would be adequate that BGX camera should work. The thing is the problem. That's why we are in EGA. You have to demonstrate whatever you want. Now what is the camera with which you have successfully got a good image even without extraordinary purpose? It's a Nokia 5530 3.2 megapixel camera. 3.2 megapixel? 3.2 megapixel. Yes sir. That's a lot of pictures. That cost may be equal to the cost of the Akash tablet itself. Some more than that. You were supposed to build an affordable solution. You were supposed to build a poor-man's-remotion, not a rich-man's-remotion. That's where the part of the lenses, the work of the lenses comes in place. We can regard this as a lot of preliminary things have been achieved. Yes. Dimensions of the attachments, etc. have been taken. The only part that is left is the work with the optics. Yes sir. So, Rajesh, will you please take help of Prashant Prakash Naidya and take this forward? So, what is the time in between? These guys are taking two months. One and a half minutes. One and a half minutes. You will be the responsible person. One and a half minutes. So, that is 15th August then. Slightly less than one and a half minutes. I would like to publicly announce on the independence day that affordable solution exists for all of them. Sure. Don't ditch independence day. Which independence? What has been the cost of the components for the attachments? The current assembly which we have designed is costing something like rupees 180. 180? Yes. But with those additional lenses? With those additional lenses, the lenses we ordered with the whole component, we had to order a camera itself to get the lens out. The camera was 600 cost. So, you can say building those simple lenses would take at the max 200 lens. Manufacturer of the lens, the lens would take 200 rupees. So, it would be 380 or 400 something. That would be 10 times less than what is the result. 400 or 3 figures. No, currently it's 200. Adding the cost of lens that is 200, it would be 380. 380. 380. I had suggested that it should be within between 250 to 400. You think it is possible? Yes, it might. It is possible. There might be a lot of doubts as you can see. But this is natural. Let me tell you, the task given to them was not an easy one. They had to actually study basic optics, which all of you would have studied at some time of the other, but I'm sure like them you would have forgotten most of it. What is total internal reflection? What is reflection? All of you are very clear on those concepts. Meaning you all remember the words. Yeah, not good enough. So, thank you very much. Let's give them a big hand. I would like to take a two-minute break to introduce two very important people. One of them is my colleague whom you might have seen or have you ever made your appearance here. So, Professor Kannan Makhalya, who is actually the coordinator of all national mission projects here, he is single-handedly responsible for convincing me to take up the Akash project when there were some problems and of course for the talk to a teacher program was conceived jointly by us under which we trained large number of teachers. Both these projects are considered fairly successful projects and that is the reason why I am given a free hand to get good students from all over the country to work like this. The other person who is actually almost the atma of the Akash project in the national mission, actually two atmas, one of them is not here. That person is Mr. Sinha, who was the then joint secretary. He is now secretary of the Bihar state government. He dreamt of both the mission and the project and the person who has worked shoulder to shoulder with him right from the inception of the mission and right from the inception of all these projects is Professor Pradeep Verma. So apart from handling these projects nationally, he also works as our direct advisor and very fortunately whenever I request him to come over here and advise us and examine things, he has always been coming. So thank you Professor Verma. Thank you Professor Kannan.


Please help us up, please help us up. Yep, y'all now, y'all now. Go sit over there by the curb. Two still in there. He's in the passenger seat.  Oh my God. Help him out, help him out, help him out. Oh my God. Oh my God. Hey man, stop moving, stop moving. We're trying to get on the, can you breathe? Can you, you can't breathe. Yo, yo.  You're gonna lift this car up right now. Yes, help, help. Someone get in there and pull him out. When he, when he, you lift it up. Help him. One, two, three, push. Pull the car up, pull the car up. Let's get under here. Come on, one, two, three, come on guys. There we go, there we go, pull the car up. Push the car up. Come on y'all, we got this. Come on y'all.


The reaction pathways of a layered perovskite, senior 3-phate 207, delta, delta ranging from 0.4 to 1.0, were studied using state-of-the-art high-speed time-resolved synchrotron x-ray techniques. It was found that the reaction progresses through a gradual single-phase structural evolution when pristine senior 3-phate 207, delta, is reduced, while a non-equilibrium dynamically disordered phase emerged at a certain point prior to a first-order transition in a PD-loaded sample. This drastic change in the reaction pathway could be explained by a change in the rate-determining step. Synchrotron x-ray techniques are applicable to various solid gas reactions and provide an opportunity for gaining a better understanding and optimizing reactions in solid state compounds. This article was authored by Takafumi Yamamoto, Shogo Kawaguchi, Taiki Kosuj, and others.