As Salaamu Alaikum, welcome to lecture number 34 of the course on statistics and probability. Students, you will recall that in the last lecture, I began the concept of point estimation and having given the basic definition of the concept, I discussed with you some desirable qualities of a good point estimator. You will recall that I discussed with you the concepts of unbiasedness and consistency. Unbiasedness k havali se aapko yaad hoga ke bunyadi concept ye hai that the sampling distribution of your statistic is centered on the parameter that you are trying to estimate. For example, if you are trying to estimate the population mean mu, then the mean of the sampling distribution of x bar lies exactly at the same point where mu itself lies. Our distribution is neither to the right nor to the left as far as the center of our distribution is concerned. It is neither to the right nor to the left of mu, but it is on mu. And students, what about consistency? Aapko yaad hain haa boh bada complicated sa expression lekin uska jo lube-lubab hai, wo itna mushkil nahi hai. Aur wo kya tha? An estimator is said to be consistent. If the probability that the estimator is very close to the parameter, if this probability increases and tends to 1 as the sample size increases, then we say that our estimator is a consistent estimator. So, wali pehda hota hai students ke consistent estimator ko hani hum iss baat ko ek desirable property kyun kahitthein. Dekhe iss pe thora sa gaur kiye. Sarai jo estimation ho re hai that is on the basis of the data that you have collected from the population, but you have not collected the data from the entire population. You have only collected data from a sample. To ye to hum intuitively understand kr satte hain aur accept kr satte hain that the larger the sample, the more representative it should be of the population. To issi hawale se hum ye bhi sochenge ke if the sample size is large, our estimator should be closer to the parameter than if it was an estimator based on a sample that was relatively small. Issi hawale se hum we have this concept and you will see that it tellies with what we would expect intuitively. Yani, to repeat what I just said once more, as the sample size increases, if the probability increases that my estimator will be very close to the parameter, then I say that my estimator is consistent and this is a desirable quality. Students, you will recall that I mentioned to you that another very important desirable property of a point estimator is efficiency. And let me now define this one for you formally. As you now see on the screen, an unbiased estimator is defined to be efficient if the variance of its sampling distribution is smaller than that of the sampling distribution of any other unbiased estimator of the same parameter. In other words, suppose that there are two unbiased estimators, T1 and T2 of the same parameter theta, then the estimator T1 will be said to be more efficient than T2 if the variance of T1 is less than the variance of T2 and students, I would like you to concentrate on the graphical representation of this concept that you now see on the screen. So, I am going to show you that both of them are unbiased estimators, T1 and T2 are unbiased estimators, T1 and T2 are unbiased estimators, T1 and T2 are unbiased estimators. So, let us say that our sampling distribution is centered on the parameter theta, students, you can see that one distribution is relatively tight and the other one is relatively wide. Now, we said that the one whose variance is smaller is the one which is more efficient. I hope that you will all have said that T1 is more efficient. That is tighter than that of T2 and we all know that if the variance is small, then of course, the standard deviation will also be small and if the standard deviation is small, then the spread of the distribution will be less and it will be a tighter distribution. Students, you should note that we are always looking for efficiency as far as point estimation is concerned. Most of them are closer to the parameter that we are trying to estimate. In other words, in a real life situation, the probability is higher that our estimator will be close to the parameter. So, this is a very important concept and one that is linked with it is that of relative efficiency. As you now see on the slide, the relative efficiency of T1 compared to T2, where both T1 and T2 are unbiased estimators, this relative efficiency is given by the ratio variance of T2 divided by variance of T1. And if we multiply this expression by 100, then of course, we can represent the relative efficiency in percentage form. And thus, we have a means of comparing different unbiased estimators of one particular parameter. Students, let us talk about sample mean and sample median. I had already told you that sample mean is an unbiased estimator and a consistent estimator of mu. Or if our distribution is normal, then the sample median is also an unbiased and consistent estimator of mu. But you will be interested to note that as far as efficiency is concerned, the sample mean is more efficient than the sample median. So if we want to choose one of the two in order to estimate mu, which one will be preferred? It is obvious that x bar is to be preferred over x tilde because of this reason that it is more efficient than x tilde. Alright, now that I have discussed with you some basic desirable properties of a good point estimator, students, I would like to discuss with you briefly the various methods of estimation that have been developed. As you now see on the screen, some of the more commonly and widely known methods are the method of moments, the method of least squares and the method of maximum likelihood. Let us begin with the method of moments. The method of moments, which is due to Carl Pearson consists of calculating a few moments of the sample values and equating them to the corresponding moments of a population. Thus, getting as many equations as are needed in order to solve for the unknown parameters. Come, let us try to understand this concept in some detail. Look, students, you will remember that we talked about that x bar is an estimator of mu, s square is an estimator of sigma square. So, similarly, higher moments, they would be estimating the corresponding population moments. For example, m3 is an estimator of mu3, m4 is an estimator of mu4. After all, x bar and s square are also moments. x bar is the first moment about 0 and s square is the second moment about the mean. So, this method of moments, the concept is that sample moments are estimating the corresponding population moments. So, we can match them. Thus, we will get equations, which can be solved simultaneously to obtain the values of the parameters that we would like to estimate. Let me explain this to you with the help of an example. As you now see on the screen, let x be uniformly distributed on the interval 0 theta. Find an estimator of theta by the method of moments. Now, in order to solve this problem, the first point to note is that the probability density function of the given uniform distribution is f of x is equal to 1 over theta such that x lies between 0 and theta. This equation, I have just presented to you, students, you may be thinking that first, when we read the uniform distribution, its formula was different. Actually, if you pay attention, this is a special case of that. You will remember that we said that f of x is equal to 1 over b minus a, where x itself lies between a and b. Now, if you keep a 0, that is, we are starting from 0 and we are going up to b, then what will my f of x become? Then I will have f of x is equal to 1 over b minus 0 such that my x goes from 0 to b. And if you keep b as theta, then what will be your equation? f of x is equal to 1 over theta minus 0 such that x lies between 0 and theta. And students, this is exactly what I have presented to you. As you now once again see on the screen, this distribution is given by f of x is equal to 1 over theta minus 0, which is of course, equal to 1 over theta such that x goes from 0 to theta. Students, this particular uniform distribution has only one parameter. If I want to estimate this one lone parameter using the method of momentum estimates, what should I do? According to what I just explained, I should compute a sample moment and match it with the corresponding population moment. And by doing so, I will obtain one equation which when I solve, I will get an estimator of theta. So, as you now see on the screen, the first sample moment about 0 that is m 1 dash is sigma x minus 0 raised to 1 over n. In other words, sigma x over n of course, that is the sample mean. And the first population moment about 0 that is mu 1 dash is given by the interval of integral of x minus 0 raised to 1 into f of x. And this integration is being done with respect to x and the limits are 0 to theta. And on simplifying, this can be written as the integral of x into f of x. And since f of x is equal to 1 over theta therefore, this integral is the integral of x into 1 over theta with respect to x with the limits from 0 to theta. Upon solving, we obtain 1 over theta multiplied by x square over 2 within the limits 0 to theta. And upon further simplification, the final answer is that mu 1 dash is equal to theta over 2. Now, matching the first sample moment with the first population moment, we obtain x bar is equal to theta over 2 or in other words, theta is equal to 2 times x bar. Hence, the moment estimator of theta in this particular problem is equal to twice of x bar. Students, aiyes mamale pe zara zyada deft me jaate gaur karte. This is a uniform distribution. Iski ek edge 0 pe hai, dosri edge theta pe hai. Aur iska jumeen hai mu that is equal to theta over 2. Isle ke wo bilkul chunke symmetric hai. Isle uska mean johai wo exact center me hoega. To is baat pe gaur ki je mu is equal to theta over 2. Aur khud theta jo hai uska aur mu ka aapis me kya relation hai. Obviously, theta itself is the double of theta by 2, yani, the double of mu. In other words, our equation is that theta is equal to 2 times mu. Ye to hai wo situation jo actually really exist karte hai for this probability distribution. Theta is equal to 2 mu. Lekkin haam agar sample data leh rahe hain aur mu hum nahi compute kr sate, because hum ne poori population ya poori probability distribution encompass hum nahi kr sate. Aur sample data leha, to hum to mu nahi nikal sate, hum to sirf x bar compute kr sate, which is an estimator of mu. To ye jo equation banti hai, theta is equal to 2 mu. Isme agar aap mu ki jaga x bar rakhdein to kya equation banti hai. Theta is equal to 2 times x bar. And this is exactly what you obtained through the method of moments. Aap ne rekhah students ke agar aap in cheezon pe hoar karein, to it is very interesting aur aap ko subject ki philosophy ko samajne mein madad miltiye. And it is so interesting ke jo cheez intuitively aap accept kareinge, mathematics ki through bhi aap ko bohi cheez mil jaati. Let me now apply this concept to another example. As you now see on the screen, let x 1, x 2, so on up to x n be a random sample of size n from a normal population with parameters mu and sigma square. Find these parameters by the method of moments. Aap ne rekhah ke statement mein hum nahi yon parha ke find these parameters by the method of moments. Lekin saap zahe rahe aap ki agar method of moments ki baat ho rahe hai, to find ka matlab hai ke estimate kareinge hum because we are collecting data on sample basis and then only we will apply the method of moments. So, students aap iss case mein how will we estimate these two parameters? Jaise ke pehle kaha tha ke we will be matching the sample moments with the corresponding population moments. But how many equations will I have in this particular case? I should have two equations. Why? Because the normal distribution has two parameters that we are trying to estimate mu and sigma square. So, as you now see on the screen, the first two sample moments about 0 are m 1 dash is equal to x bar just as before and m 2 dash is equal to sigma x minus 0 whole square over n, which upon simplification becomes sigma x square over n. What about the corresponding moments of the normal distribution? These are mu 1 dash is equal to mu and mu 2 dash is equal to mu 2 dash is equal to sigma square plus mu square. Now, this second equation is particularly important and you will realize that we obtain this equation from the basic equation that we have already discussed in this course. The one that relates the moments about the mean to the moments about arbitrary origin A or the moments about 0. We have already studied that mu 2, which is the same thing as the variance is equal to mu 2 dash minus mu 1 dash square and since mu 1 dash the first moment about 0 is the same thing as the mean mu. Hence, our equation becomes sigma square is equal to mu 2 dash minus mu square and taking mu square to the other side, we obtain mu 2 dash is equal to sigma square plus mu square. Now, in order to obtain the estimators of mu and sigma square by the method of moments we match the sample moments with the corresponding population moments and thus we obtain the following two equations. Equation number 1 mu is equal to sigma x over n and equation number 2 sigma square plus mu square is equal to sigma x square over n. Solving these two equations simultaneously, students we obtain mu hat is equal to x bar and sigma square hat is equal to summation x minus x bar whole square over n, which is nothing but capital S square the variance of our sample. You have seen that the method of moments through estimators, they are none other than what we have been discussing and we are familiar with and that is the simple mean of the sample x bar and the simple variance S square. This is the method, very, very simple. If you have only one equation, you need just one equation. If you have to estimate two as in the case of the normal distribution then you should form two equations and solve them simultaneously and so on and so forth. So, students although it is very simple, but there is one point that is to be noted that moment estimators are generally inefficient, that is not generally not very tight. So, that is a shortcoming of this method. The method that I will discuss with you next very briefly is the method of least squares. This is a method by Gauss and Markov and it is based on the theory of linear estimation. As you now see on the slide, an estimator found by minimizing the sum of the squared deviations of the sample values from some function that has been hypothesized as a fit for the data, such an estimator is called the least squares estimator. Students, I think you are trying to confuse it completely, but there is no need to do that because you will recall that in lecture number 15, I have already discussed with you this concept when we talked about regression. You remember that first of all we made a scatter diagram or our points, our graph cupor I, if we note that this seems to be a linear pattern then we decided that we will fit a straight line to this particular data set. That particular line, which is the one for which the sum of the squares of the distances between the points and the line that sum is minimum. Exactly this is the method and the principle of least squares and what you just saw on the screen is telling with what I just explained. Students, why is this being called a method of estimation? With reference to regression that I just discussed, you will be interested to know that the line that we are fitting to our sample data, actually this is an estimate of a line that we would have obtained, if we had not collected only a small data set on sample basis, but if we had access to the entire population of data points for that particular situation. That is, if we do not have 5, 7, 10, 12 or 20 points, but if we have 1 crore or half points regarding those two variables that we are correlating with each other and regressing one on the other. If we have 1 crore or half points, then the line that we get in terms of the means of the y values corresponding to various x values, that true line would be our estimate of this line and we have established this line by the method of least squares. In this course, I will not be going into too much mathematical detail, but I would like to convey to you a few points, so that if you are so interested, you may study in further detail on your own. The next method that I would like to discuss with you is a very, very important method of estimation. This is known as the method of maximum likelihood. This was introduced by the great statistician Sir R. A. Fisher in 1922. And although the technique and the concept is a bit advanced and it involves the concept of the likelihood function, which I will not be going into the details of, I would like to give you a basic idea about the core of this concept. As you now see on the screen, according to this method, we would like to consider every possible value that the parameter might have and for each value compute the probability that the given sample would have occurred if that were the true value of the parameter. That value of the parameter for which the probability of a given sample is greatest is chosen as an estimate. Students, once again, of course, you want to get confused, but again I would like to say that step by step, step by step, step by step. Now, one example is that if we want to estimate the proportion of success in the population for any particular population. Now, you know that if we say that every possible value of parameter to consider, then in this case, P that can have any value from 0 to 1, you will agree that proportion of success or probability of success cannot be less than 1 or not more than 1 because 1 means 100 percent. So, we have determined that our parameter, which we are going to estimate, will be brought somewhere between 0 and 1. Now, the question arises which value between 0 and 1 which we can regard as the value. Now, we have drawn a sample, a sample materialized. So, if the information in that sample says that this information has a particular value of this particular parameter, you see, the concept is that of maximum likelihood. As this given sample is present, what is the value of P that is more likely? You see, there is an example that if in reality P is 0.9, then my sample that has come in, if P hat is coming in 0.3, then this is not happening with it. If the proportion of success in the population is 90 percent, then why did my sample come in 30 percent? It should have been relatively high in the sample. This is intuitively understandable. So, the discussion is that once again without going into the mathematical details which are quite advanced, I just wanted to convey to you a basic idea. We are trying to say that given this particular sample, what is the value of the parameter that is most likely in the light of this information? Having said all this, I will make it clear here that this is a very non-mathematical way of trying to explain it. The mathematics involves differentiation because as you have studied in pure mathematics, when you are trying to find the maxima or the minima of a function, you do take derivatives. So, we will talk in that way, which is evident that scientifically speaking that is the best way. So, we will talk in different ways. But once again, the object of my discussion is to give you a preliminary intuitive idea that is involved in this particular method. Students, let me give you a few examples of the estimators that we obtain by the method of maximum likelihood in various situations. As you now see on the screen, for the Poisson distribution given by e raise to minus mu, mu raise to x over x factorial, the maximum likelihood estimate of mu comes out to be x bar for the geometric distribution given by p into q raise to x minus 1 such that x is equal to 1, 2, 3 and so on. The MLE that is the maximum likelihood estimator of p comes out to be 1 over x bar. In other words, the MLE of p for this particular distribution is equal to the reciprocal of the sample mean. For the Bernoulli distribution given by p raise to x, q raise to 1 minus x such that x can take either of the two values 0 and 1, the MLE of p comes out to be x bar. And having discussed these discrete situations, we now go to some examples of continuous probability distributions. So, for the exponential distribution given by theta into e raise to minus theta x such that x is greater than 0 and theta also is greater than 0, the MLE of theta is 1 over x bar, the reciprocal of the sample mean. For the normal distribution with parameters mu and sigma square, the joint maximum likelihood estimators of mu and sigma square come out to be x bar and s square. Capital s square which is not an unbiased estimator but which is consistent. Students, in this course we have discussed many times that the normal distribution is one of the most frequently encountered distributions in practice. So, you have seen that for this frequently encountered distribution, the simplest things that we compute, the sample mean and the ordinary sample variance, they are the maximum likelihood estimators of mu and sigma square. That means, the simplest quantities we compute without thinking of all these advanced techniques and these very advanced criteria for good methods of estimation. It is so interesting that these simplest quantities in very, very criteria fulfill. X bar is unbiased, consistent, efficient and capital s square although it is not unbiased but it is consistent and efficient. So, now we will apply this on a practical example. As you now see on the screen, it is well known that human weight is an approximately normally distributed variable. Suppose that we are interested in estimating the mean and the variance of the weights of adult males in one particular province of a particular country. A random sample of 15 adult males from this particular population yields the following weights, 131.5 pounds, 136.9, 133.8 and so on. Find the maximum likelihood estimates for theta 1 equal to mu and theta 2 equal to sigma square. Now, students in order to solve this problem, the first thing that we note is that this sample, very small sample of size 15 has been drawn from a normal population with mean mu and variance sigma square. It has been mathematically proved as already discussed that the joint maximum likelihood estimators of mu and sigma square are X bar and capital S square. So, all we need to do is to compute X bar and S square for this particular data set and doing so, we obtain X bar is equal to 133.43 pounds and S square is equal to 5.10 pounds squared. Students, of course, we can now very confidently say that these are the maximum likelihood estimates of the mean and variance of the population of weights in this particular example. Students, we have discussed at some length the concept of point estimation. Point estimation kya hai? A single quantity that we compute from the sample in order to estimate the corresponding parameter. Lekin aap gaur karin to iss method me ye limitation hai that in any particular real situation when we have a particular sample and we have computed this quantity. We have no way of knowing how close or how far this particular estimate is from the parameter that we are trying to estimate. We have discussed in detail that X bar is an unbiased estimator of mu. Iska mafum kya tha? That if you do not compute just one X bar from one sample, but if you draw all possible samples of a particular size from that population and you find X bar for every one of them. To bo jo all possible X bars honge unki jo mean value hai that is identical with mu. But in a real life scenario this does not help us tremendously. Kyuke real life me aap all possible samples draw nahin kar rahe.  Ho sakta hai ki ye X bar mu can iss deek hi ho in which case you are lucky. Lekin ye bhi to mumkin hai na, ke it is quite far and it is towards the edge of your sampling distribution of X bar. And if it is towards the edge then it is quite far away and the distance is quite large from mu. To ye shortcoming hai of point estimation that you do give a quantity as an estimate of your parameter. But you are not able to attach a statement with it as to how confident you are that it is close to the parameter. Internal estimation is that procedure in which you are able to give not one value, but a range of values within which the true population parameter value is expected to lie. And you are able to give a level of confidence along with this interval. As you now see on the slide a confidence interval is an interval computed from the sample observations X1, X2 so on up to Xn with a statement of how confident we can be that the interval does contain the true parameter. Let us develop this concept with the help of the example of the Ministry of Transport test to which all cars irrespective of age have to be submitted. You will recall that this test looks for faulty brakes, staring lights and suspension and it was discovered after the first year that approximately the same number of cars had 0, 1, 2, 3 or 4 faults. Students, aapko yakinan ye example yad aagya hoga. Or ye baat importantly yad ki jhe when we drew all possible samples of size 2 from this uniform distribution our sampling distribution of X bar was triangular. But when we increase the sample size to 3 our sampling distribution was like something like a normal distribution rather than triangular. And when we increase the sample size to 4 the shape of the distribution became even more like a normal distribution. This example ki baat me dubara ish liye kar rahi hoon ke ye jho normality hai of the sampling distribution which of course also is presented formally by way of the central limit theorem which we have already discussed. I wanted to draw your attention to this fact once again. Ke aksar okaat in real life situations. Hamara sample size 2, 3 or 4 to nahi hoega. It will be much larger. Aur agar 4 size pe hum dekh rahe hain ke it is something like a normal. To zahere hai ke size 30, 50, 100, 500. Ispe to wo usse bhi bohot zyada normal hogi. So, the concept of confidence interval that I am now going to present to you is based on this basic point that in many situations when we are trying to estimate mu by computing X bar our sampling distribution of X bar can be regarded as a normal distribution and hence I will now derive for you the confidence interval for mu based on this normal distribution. Students aap kahenge ke derivation karne lage hain. All through I have been saying that in this particular course I am not going to do derivations but I will be simply giving you the basic idea and the basic concept and then we will be applying these concepts to real life situations. Yes true. That is exactly what I have been doing most of the time and I will be doing in the next lectures too but students believe you me if you concentrate on this one derivation that I am going to do now for you. You will be at ease with the concept of interval estimation. As you now see on the slide when sampling from an infinite population such that the sample size n is large X bar is normally distributed with mean mu and variance sigma square over n. Hence the standardized version of X bar that is Z equal to X bar minus mu over sigma over square root of n this is normally distributed with mean 0 and variance 1. Now for the standard normal distribution we have area between 0 and 1.96 equal to 0.4750 as indicated in the area table of the standard normal curve and therefore the area from 0 to minus 1.96 is also 0.4750. This implies that the area between minus 1.96 and 1.96 is 0.95 and since area represents probability therefore we can say that the probability that Z lies between minus 1.96 and plus 1.96 this probability is equal to 0.95. Now substituting X bar minus mu over sigma over square root of n in place of Z in this equation we have probability that minus 1.96 is less than or equal to X bar minus mu over sigma over square root of n less than or equal to 1.96 this probability is equal to 0.95. Let us rewrite this equation in such a way that we take the term sigma over square root of n which is in the denominator of the central expression we take this term to the expression on the left and the expression on the right and by when we do that of course it will no longer remain in the denominator but it will be attached to minus and plus 1.96 respectively in the numerator. Hence our equation now becomes the probability that minus 1.96 into sigma over square root of n is less than or equal to X bar minus mu is less than or equal to 1.96 sigma over square root of n is equal to 0.95. Students it is extremely simple. The moment you do that the term does not remain in the denominator of course it will attach in the numerator or in the main expression in the left hand side term as well as in the right hand side term. Now there are just a few more steps to this derivation and then we will arrive at our confidence interval. As you now see on the slide we have probability minus 1.96 sigma over square root of n less than equal to X bar minus mu less than equal to 1.96 sigma over square root of n this whole probability equal to 0.95. Abhi thori der pehle ham sigma over square root of n ko left or right sides pehle gaythe ab hum jo term X bar hai in the middle usko bhi lekar jaana chahthe to the left hand side and to the right hand side. Chunke middle expression me X bar is being added to minus mu. Isliye jab hum usko left hand side pehle gaye to the left hand side pehle gaye to the left hand side pehle ham. So, we obtain the probability that minus X bar minus 1.96 sigma over square root of n is less than or equal to minus mu is less than or equal to minus X bar plus 1.96 into sigma over square root of n this whole probability is equal to 0.95. Chunke ab hamare central expression me minus sign aah rahe which is not extremely wonderful for our purposes. Therefore, we would like to multiply the entire expression inside the brackets all the expressions by the minus sign, but we all know that the moment we will do that the less than equal sign will interchange with the greater than equal to sign and hence students we now obtain the probability that X bar plus 1.96 sigma over square root of n is greater than or equal to mu is greater than or equal to X bar minus 1.96 sigma over square root of n this whole probability is equal to 0.95 students. This derivation we have just done actually we have reached our confidence interval but we want to do one more step and what is that we have said that something is greater than mu and mu is greater than something instead we want to do another reverse order. We would like to say that something is less than mu and mu is less than something. So, what should we do? Just do this, reverse it. Write the term on the right hand side and write it on the left hand side and bring it on the right hand side. Naturally what you will do is that your greater than sign will become less than sign again. For example, if you say that 3 is less than 4 is less than 7 this is equivalent to saying that 7 is greater than 4 is greater than 3. So, as you now see on the screen the probability that X bar plus 1.96 into sigma over square root of n is greater than or equal to mu is greater than or equal to X bar minus 1.96 into sigma over square root of n this probability is equal to 0.95. This statement is equivalent to the statement that the probability that X bar minus 1.96 into sigma over square root of n is less than or equal to mu and that is less than or equal to X bar plus 1.96 sigma over square root of n this probability is 0.95 that X bar minus 1.96 into sigma over square root of n is less than or equal to mu and that is less than or equal to X bar plus 1.96 sigma over square root of n. These two quantities that appear inside the bracket on the left hand side and the right hand side they are known as the lower and upper limits of our 95 percent confidence interval for mu. Students, that the probability is 95 percent that the interval X bar minus 1.96 sigma over square root of n to X bar plus 1.96 sigma over square root of n this interval will actually contain mu the parameter that we are trying to estimate and that is why students this is called a 95 percent confidence interval. Of course, we can have 99 percent confidence or sometimes we may even be happy with 90 percent confidence, but then as you saw in the derivation then those numbers 1.96 and minus 1.96 will be replaced by other numbers which we will get from the area table of the standard normal distribution. A or point note or in a real life situation many times of course, sigma is unknown. So, what do we do? We replace sigma square by its unbiased estimator small s square which you now see on the screen as indicated last time it is summation X minus X bar whole square over n minus 1 and in this case our interval becomes X bar minus 1.96 s over square root of n to X bar plus 1.96 s over square root of n. Students, in today's lecture I discussed with you the desirable property of efficiency then we went on to various methods of point estimation last but not the least we have started the concept of interval estimation. In the next lecture I will be discussing with you various real life applications of the concept of interval estimation. In the meantime I would like to encourage you to practice and to study the concepts involved in point estimation. My best wishes to you and until next time Allah Hafiz.


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So if you guys like this video be sure to subscribe Also, thank you to skill share for sponsoring today's video If you guys didn't know skill share is an online learning community with thousands of inspiring classes for creative and curious people Skill share offers a creative class is designed for real life and all the circumstances that come with it These lessons can help you stay inspired express yourself and introduce you to a community of millions It's also great because if you're anxious you can explore classes that may help you express what you're feeling through creative self-discovery Also, if you're uncertain about what's next a creative challenge or productivity class may offer some helpful structure For setting small goals and feeling a fulfilling sense of accomplishment something I've really loved about 2020 is I've taken up a lot more hobbies of things I didn't even know that I was gonna love so much like cooking and honestly floral arrangements It's really great to take classes on different topics to see what you like And that's also awesome to even get better at the craft that you already know you love So you guys can tap into the support of fellow creatives who provide encouragement communication and inspiration Drawing writing and journaling classes may be a great way to help manage stress practice mindfulness and feel connected to one another I mean, it's so cool There's classes that help you with drawing with illustrator with Photoshop even interior design classes I love interior design, so it's like one of my favorite things also if you're really into Instagram They have a lot of classes on there that are really really helpful I'm pulling up the class that I took but I took the interior design at basic simple steps to perfect your space I'm still in the process of doing my house. I'm actually about to redo my entire room So I thought it would be the perfect class for me I don't know about you guys, but it's really easy for me to get bored Just being in the house so much lately and I really like the like self-expression that I get from these creative classes It's a really nice escape, but it also adds value, which I love the first thousand of you guys We'll get a two-month free skill share premium membership. You guys can check out all the classes You really can't lose. It's a great offer. So click the link down below. All right guys So moving on into I think we're gonna start with clothing. Okay I've got three pieces of clothing. The first would be at my court score I'm just going to insert some photos of me wearing it I feel like I've already included this in a favorites video with all my outro voices stuff But the court score is such a good buy because you can actually dress it up And then you can also like actually work out in it, but it's really Really good for the summer because I don't know about you guys. I don't know where you live But it's so freaking hot in Texas It like makes me absolutely miserable and the course core is amazing because you walk around and you look cute But you're actually wearing like athletic wear So it's just like 10 out of 10 cannot recommend enough I will link a few more of my outro voices favorites down below because that is my like number one summer must have my wardrobe Because it is so hot. Okay something that is like really just totally opposite. I got my first boys lie set So this is the top my sweats. I don't have my sweats on me But I'll insert some pictures. I am absolutely obsessed I have seen boys lie on Instagram for the longest time and I just fell in love with the set I think it is the cutest thing I've ever seen in my entire life I think I cannot stress that to you enough since wearing this I have bought two more sets because they are just so cute The quality is next level. I know I'm gonna get so much wear out of these I just love them genuinely. It's probably my favorite brand right now for clothes. I will link them down below They sell out a lot of the time and then most things are on pre-order So I pre-ordered this and they got it like a month later But just the best clothes if I could wear a different boys lie set every single day I would okay, the next thing I have are some girlfriend jeans. So these jeans are so comfortable Okay, I got these originally in a size 28, but then I got them taken in so I would say I'm typically a 27 or 28 and I had to get these taken in so keep out of mind They have a seam in the back, which I just think is so cute. They're the most flattering jeans I love them a girlfriend can really do no wrong in the denim department like they by far in my opinion have the best jeans And I love them. So I'll also have those linked down below They're kind of hard to find the exact pair, but I will lay them down below Honestly, it's just girlfriend denim as a whole. I love the shorts. I love everything And I am so picky when it comes to denim shorts, and I love theirs. Okay moving on to shoes So these will probably come as no surprise to you. Wow. These were my birthday gift to myself. So cute So they're Jeffrey Campbell. I got them on revolve. I got them I think like half off. So if they're still on sale pick a pair up. They're so comfortable. They're so cute there I just love the color. I think they're really unique and I'm just absolutely obsessed with them Western is in and also I'm a Texan, but like no one here really dresses like that. It's actually just me So I'm the one who gives us that like people think that I ride my horse places You know what I mean the next pair of shoes I have are these sandals from Rothes. I'm not a huge sandals girl I don't really like them for the most part I'm really picky when it comes to sandals, and I love these. They're really cute. They're really comfy County goes with my Like country club chic look, you know in the next pair of shoes. I just wore these to the lake. So bear with me They're definitely dirty They need to be washed, but I wanted to include them in the video these champion sneakers. They're so cute I got them. They're only $60 and I got them post them on my Instagram story And everyone's like where's the link and then they disappeared off the urban website. So I will try to find them online I know there's a few other colors, but they're so comfortable and they're so cute and they're cheaper than air forces or any of those Other just like classic white sneakers, and I actually like these better. I think they're cuter and it's more fun So I love those. I will try my best to find them for you. So I got my first year who are set I did a IG live workout with daylight and they sent me this set and I think it is the Cutest set ever first off. It's bright pink and like guys just look at that look at the sports bra It's so cute. So the bottoms are really cute. I got both the top and the bottoms in a size medium I love the color and I love the color. I've been wearing a little more color lately I guess but I still am like more of a neutrals girl and I am obsessed with that set. I think it's so cute It's so comfortable It's even fun to like wear in the morning when you're like going to grab coffee with a friend or something Love the set 10 out of 10 recommend I want a lot of other year of ours sets as well also like even the inside of this is so cute I want more. I only have this one We are going to start with skin care first product. I have is the ordinary squalene. This stuff is legit $7 I actually need to buy another bottle. It is next level. It is the most hydrating oil ever I feel like a lot of the time, you know when you put a serum on that's a good less expensive serum And it makes your skin just feel like papering dry and gross. No, this stuff is amazing It is legit $7 guys. I love this I put this on every morning and then I like Massage my face out with this that I always forget the name of it I will literally never remember the name of it when I'm filming when I'm not filming I always remember the name and then when I'm filming it just you know I showed how I apply this in my latest morning routine But it is so good and then it sculpts your face so well and you're like snatched, you know I don't think I've ever said snatched in my entire life and then every morning as always I know I've talked about this so many times But I just like couldn't not include it because it is my number one holy grail product that is like ever existed It's the super group glow screen sunscreen. So it's SPF 40. It leaves your skin looking beautiful It leaves it really like lively awake bouncy Just dewy very moisturized It's just like the most beautiful finish and it is from the sunscreen Also, it's great because it actually makes me wear sunscreen every day now I picked up this perfume from a favorite the kind. It's gonna Wow Smells so good. It's from the brand west third brand and it the scent is banded outlaws It smells so good. They compared it to lay Lobo's scent, which I actually agree with but it's definitely a more affordable price So I love this. I think the branding is super cute I know that perfumes are kind of hard to like describe to you guys because you can't smell But trust me. This is a great perfume hair products. Okay. I have one that I love Okay, so this function of beauty hair serum I'm sure you guys have seen them all over because everyone on YouTube works with them But they have the best hair serum This is the best product I've ever used on my hair and it's kind of tricky because these are all customized So I'm sure if you guys got your own hair serum, it would be customized You so my hair is really dry when I put oils in it either gets like super stringy or just like PC and gross and too oily and this is like the best thing ever because I can put as much as I want in it And it just leaves my hair way more moisturized and it smells so good I would have always get the scent eucalyptus with them But next level best hair product I've ever used cannot recommend this enough recently got this sunbomb Tinted sunscreen lip balm in the color sunset Cove. So cute I'm wearing it on my lips right now with a lip gloss. I'm about to show you But this is just the perfect amount of color but also it protects your lips, which I love I'm wearing it This lip gloss on right now. It's the beauty counter lip gloss in the quartz shimmer So pretty so moisturizing these lip glosses are by far the most moisturizing lip glosses I've ever worn your hair doesn't get stuck in it. I'm like a really big snob when it comes to lip products, too And this is like the best the capari lip glossy I know I've talked about this before but it is so bomb that the capari lip glossy the I used to use the one that Didn't have these shimmer. This is on the shade at birthday Sue, but it is just so incredible It's a lip balm that really hydrates your lips also gives it like the most perfect beautiful nude sheen I love it. It smells so good. I put so many people on the capari stuff So many of my family members love this stuff. It is just so good. The next thing I have is this real technique sponge So if you guys use beauty blenders or anything like that stop and use the real techniques sponge I got four of those for like $14 in my opinion There's so much better than the beauty blender my mom my sister everyone I know uses them and I just love them I know it's kind of hard to branch off from Beauty Blender because sometimes you're like Oh, I just don't think it's gonna be as good and it's gonna feel like a weird harsh sponge No, no, that is the best one. I will have it linked down below Okay, next thing I got I picked up these two notebooks from anthropology on my birthday I've been loving them I love notebooks because these are like really really colorful for me and I love them I use this just like a prayer journal in the morning super cute love the pattern This I just put next to it all the time because it looks cute together But I don't know what I'm gonna use it for so comment down below what I should use this notebook for Oh my gosh guys. I totally forgot the best product. Oh my gosh, okay? Okay, if you're gonna buy any like makeup or skincare products from this video You need to do the hourglass powder this powder It's next level. I've used this before it's the dim light powder I this is always been a holy grail of mine I just haven't picked it up in the longest time and I don't know why but it is one of those products that you Think is kind of like oh, I don't need that It's not like I have to have that until you buy it and then you literally have to have it because it makes your skin Look so healthy so glowy so pretty it gives you the best sheen It just it kind of blurs out your skin as well I don't even know how to describe how good this pattern is to you like you just absolutely have to go buy it It's next level also my nails are so cute guys myself tanners really messed up on my hands I don't want to talk about it, but at least my nails are cute, you know My phone is in that one. Oh, I found it another thing accessories I got a new pair of Jennifer Fisher hoops for my birthday love these I forget the size and the actual name of it They're really cute They're a lot smaller with my other pair and they're just better to wear like I can wear them when I work out and stuff And I don't notice I Jennifer was sure to me is so worth the money You don't even feel that you're wearing hoops. They're way better quality. I just love Jennifer Fisher anything like Seriously just next level, but they are pricey for sure So that's not something you want to some money on I'll link down below a pair that are less expensive invest It's just something that like I invest in because I'll wear it every single day. Okay. Also. I've been wearing bracelets lately again Again guys my hand. I'm so sorry, but I have this Christian Dior this bracelet right here is a Christian Dior bracelet we got it in New York as friendship bracelets last December which is so fun and cute and then I have this other Bracelet on that's so cute. That is only like $20. It's way cheaper than the other one But that's it's from beaded by Yaz on Instagram, and I just think it's so cute So go support her small business my book favorite for the month I don't know where my kindle went, but obviously that's always a favorite I'll have a link down below like nothing will make you read or just love your life more than a candle oasis Or just even the other candles so bomb My book favorite of the month would be heart bones by Colleen Hoover It's her latest release she really released it like two weeks ago, but I read it in one sitting It's so good, and it's also based off of the coast in Texas, so it's pretty cute You know so Texas forever, but seriously like I just Loved that book. It was so good. I did not see what happened coming at all Like that was the last thing I saw coming And I really enjoyed it you guys ever want any more bookrex or anything like that You guys can just follow my Instagram because on my book highlights. I'm always sharing new reads with you guys I'm a book probably like 60 of 2020 at this point It's like all I do is read so that is it for today's video again At the first 1000 of you guys who click the link down below will get two months free of a skill share premium membership We love life long learners over here, and you guys can become a member again two months for you guys click the link down Below why not you know any mean anyways hope you guys enjoyed today's video if you guys did Let me know by giving it a thumbs up comment down below where you guys are watching this video from I love you guys so much And I will see you soon. Bye


Hello and welcome to the WISIS Forum 2019. We are celebrating our 10-year anniversary this year and as you all are aware the WISIS process is built around the framework of WISIS Action Lines and there are several components that make the WISIS process effective and inclusive. We are going to be talking to some representatives of the WISIS process today and the theme for today's talk is aligned to the theme of the high-level political forum 2019 which is empowering people through inclusiveness and equality. Good morning Sophie.  What role does collaboration in this area play to ensure equality and inclusiveness? Good morning Kitangeli and thank you for inviting me for the interview. Indeed equality and inclusiveness. We are in the age of digital transformation. If we want to bring in the bottom of the pyramid everybody have everybody connected. We also need to see how that connectivity can benefit them so they can be included in the digital economy. For that ICTs are really the oil of the motor. It's the oil that makes society and the economies transform. And for that we need collaboration, collaboration across the partners, collaboration across the sectors and collaborative regulatory measures because that collaboration, the discussion and the talking to each other and ensuring that together we find the innovative solutions to really include everybody in an equal way in the digital economy. It's a foundational element. Thank you very much Sophie. Of course collaborations, partnerships, networking for win-win situations is the key for this forum. Now we are moving to our Action Line facilitator for Action Line C2. It's ICT infrastructure. Good morning Desiree. My question to you would be what are the new technologies that are emerging to ensure equality and inclusiveness in this area? Good morning Kisanjari. The technologies are improving as you have noted. After 10 years anniversary of the WISIS we are doing some improvement in terms of broadband. Broadband, if we go to rural areas that's where we make an impact and the inclusiveness can be a reality. So new technologies, we have broadband technologies. This includes many standards developed by our department in ITUT on optical cables, low cost optical cables and also other broadband technologies which are standardized, other not standardized like DOCSIS but also 5G coming in operation these days and this really will make a difference. But the key issue here we need to have clear policies on broadband also business model. The business model which can be sustainable even in rural areas. Thank you. Thank you very much Desiree. Connecting the world especially the rural areas is crucial for the Action Line C2 in ICT infrastructure. We have here with us today also our regional representative to give us a regional perspective of why it is important to implement WISIS Action Lines at the regional and national levels. Good morning Yaroslav. My question to you would be how can we strengthen regional cooperation for equality and empowerment of people? When the global leaders agreed on the 2030 Agenda for Sustainable Development all countries committed to achieve SDGs by 2030 and also in line with this change the UN system is adapting to make sure that the real impact is happening at the national level and that the real action is happening at the country level to address the challenges of the countries. This is the reason why the WISIS framework is so important for assisting the countries in strengthening and amplifying the impact of the ICTs on SDGs. A lot of discussions at the national level are happening in field of health, education, governance but more and more we are hearing that the ICT is this central point of all those projects and therefore here we're coming to the need and necessity of alignment of the WISIS process with the SDGs and more importantly on strengthening the regional implementations. This is the reason why the all action line facilitators are so eager to work together with the Economic Commissions of the United Nations and to make sure that the ICT component is very strong in the original development for us and that the ICT component is essentially the most important component in the all UN development assistance frameworks which now are rebranded but still are focusing on the addressing the national challenges. Of course there is plenty of different national initiatives, projects and supporting the countries but we are working with the all UN systems and sister agencies to support all countries at the regional level. Thank you very much Yaroslav. Regional, national and international collaboration in fact is very important for the success of the WISIS process and here at the WISIS forum we have more than 3000 stakeholders who represent the WISIS stakeholder communities from all these different stakeholder types. A very important part of the WISIS process is also the partnership on measuring ICT for development and this is facilitated by a group of UN agencies. We have a representative from the partnership Miss Esperanza. Esperanza what role does the ICT for the measuring partnership for ICT play in ensuring equality and empowering people? Thank you Gitanjali so the partnership was formed 15 years ago with its original objective of improving quality and quantity of ICT statistics in countries. So we have been very involved in ensuring that this goal is achieved first by assessing the monitoring of the WISIS targets where we look at the WISIS target indicators that were defined few years back when WISIS just started but most recently we had embarked on a work through our task group on ICTs for SDGs where we are defining indicators that could be used to monitor the implementation of the SDGs so what will be the role of ICTs in achieving the SDGs and through this work we have come up with a number of indicators which we presented actually in the session that we organized on Monday which is open to all WISIS stakeholders they can provide comments to this list of indicators with an objective that the implementation of the SDGs could be speeded up by the use of ICT so we want to measure how ICTs could be instrumental in achieving the SDGs so that is the current work that the partnership is focusing on and we are counting at the different WISIS stakeholders to provide comments to those indicators and to use them when those indicators are available so that they will be able to assess the implementation of the SDGs Thank you Thank you very much We heard from all our representatives that ICTs are crucial to achieve the sustainable development goals and different processes within the World Summit on the Information Society are working to ensure that the implementation activities are impactful Thank you and wish you a great day


The Depart Company, maker of better things for better living through chemistry, presents the Cavalcade of America, starring Jean Tierney. Here's Jean Tierney. Tonight on Cavalcade, I see a woman who is suddenly in prison behind a terribly, deadly, nearly starlit. This is the true story of that woman, and how she came from behind that wall. Jean Tierney, as Marie Haynes. You're in for all the silence. You never know when it's going to happen. You lead your life normally.  That's how it began with me. Yes, there was a winter dance at the Cosset Plaza in Boston. I was a sophomore at Simmons College. I was young and I was happy. And it was a big dance of the winter season. Marie? I never would have to tell you. What? Let me show you dance. Nope, not the way. Not another one like Marie Haynes. Oh, really, not the way. Anyway, let's not talk at all. Let's just dance. I love to dance.  You know something, Flo. The only thing wrong with tonight... I'm not in... Where's it Henry wasn't there? Oh, no, not Henry, Heiner. He is nice. Marie Hayes in 10 seconds... That's very good, I bet. You ever gone to sleep as I did that winter night in 1926? My flesh tingled, I was warm. I felt asleep dreaming of the voices in the music of a sounding world. It did go off moving. The roommate has nothing more serious than the case of influenza. The doctor, she can't... Yes, I know, she can't hear. Happens. The infection spreads. She'll get better. Now just see that she takes these pills. Get plenty of fluid into her. Well, nothing to worry about, not a thing. I saw his lips move, but I didn't hear a single word he said. When your ears have been busy bringing you the sounding world for all your life, the absence of sound, the abrupt unexpected end of sound is like the death of consciousness. That's how it was for me in 1926. I got well, but my hearing had only partially returned. In order to hear, I had to strain all the time. It was like having to stand on my toes while everyone else was relaxed and comfortable. Just sit tight, Marie, darling. I'll get you an eggnog. Eggnog? Yes, Marie. You need building up, darling. Do I, Mother? I'm really much better, you know? That's fine. Are you glad to be home again? What? Iggy Cleveland will welcome sight again. He didn't say so. Mother, you did ask me if Henry Heiner was signing to call tonight. That's what you asked Mother, wasn't it? Yes, of course, Marie. I'll have your eggnog in a moment. Darling, there's a new doctor in town. I hear you, Mother. There's really no need to raise your voice. Oh, excuse it, darling. I was saying that there's a new doctor in town who seems to have a national reputation as an oncologist. That means ear specialist, you know. Why don't you and I pay him a visit tomorrow morning? Now, Marie, just one more time while I strike the tune fork like this, at places here, like this. Yes, Marie? Exactly the same as before. Not much different? None much. No. I think that will be all for now. She's really considerably better than she seems. Wouldn't you say so, Doc? Oh, yes, Mrs. Hayes. Only a slight impairment, which will improve with time. Nature, you know. Evade a wait.  Just a moment, please. I'm going down. Up, going up. What's the door, please?  I'm going down. This car goes up. What's the matter, lady? Wake up. Hi, darling. Mother. Darling, I can't show the neighbors. Mother, I'm sorry. I didn't expect you in before. Oh, darling, darling. You were never afraid to be alone before. You live among friends, Marie. You don't have to bolt the door in broad daylight. You don't have to. How are you, darling? Fine, Mother. Just fine. I had become afraid. Afraid of not hearing. And not being able to hear, I listened increasingly to the fantasies of my imagination. I imagined conspiracies against me everywhere. I bit a heart. Two diamonds. What were they whispering for? Waiting for you, Marie. What was that smile for? What were they saying about me? Two diamonds, Marie. You certainly can be mistaken about a person who's known all your life. What do you mean? You grow up thinking a person is pretty quick on the trigger. Oh, for heaven's sake, have a little piece, Marie. Oh, you can say anything you want. Everybody knows she's deaf as opposed.   I pretended that I hadn't heard. That was foolish. But even more foolish, I pretended that I heard when I heard nothing. I wanted to be normal. And a normal woman has two ears. Small ears, long ears, thin ears, thick ears, pretty ears, silly ears, but functioning ears, ears to hear the sounds of the world. When the wall of silence begins to close in, one by one, all the shared pleasures of life are taken from the heart of hearing. First to go is music, the conversation of friends, the voices of birds, the drip of water, all that remains is the emptiness of vanity, which forbid truth. I sound increasingly left me. I went from doctor to doctor. Listen now. Now we shall try the whistle from this side. Pay attention, please. Did you hear that, Miss? Oh, yes, Doctor. Much better. Could you blow it a little louder? That was loud enough, Miss Hays. What am I saying? Much better, Doctor. Miss Hays, you didn't hear a thing. I am writing down a name and a thread. Take it. Go to Miss Elliott. She teaches lip-reading. A woman is created whole. She has hands for touching and lips for speaking and a palate for case. A nose is intended for smell and eyes for sight. Ears for hearing. We are created whole. The world is a whole world. And now, now I was a partial human being.    And you know the fright of silence. Who's there? Is there someone at the door? A young American woman, Marie Hays, has lost her hearing and finds herself in a lost world alone, behind a wall of silence. Panic is also a wall. When the panic left, I felt better. And I heard a little better. But it was a black time for me. And it was at that time that Henry Highland came and asked me to marry him. All right, Marie, so you don't hear. Henry, I may get wind. Yes. You can't marry someone totally deaf. I don't want to marry your ears, darling. I want to marry you, hearing or not. Hearing makes no difference. It isn't true. You have to hear. You have to hear what a husband says. You have to hear children when they fall down, when they're sick, when they cry. I was gambling with the safety of my children, my children's children. I didn't know. No one tells you these things. Yes, I became Mary Hayes' child. It was easy to be happy with Henry. He understood. He pitched his voice to my needs. He spoke clearly and directly to me. He never talked to me from the next room or from behind me. You young folks have done this room up very well. John, what a sweet prayer. Marie, where did you get it? Darling, Mrs. Lewis likes the print as much as we do. Oh, my thank you, Mrs. Lewis. I bought it yesterday. A real bargain. Marie buys only bargain, whether she needs them or not. Ha, ha, ha. Blastness should be heard, not seen. It's hard to share happiness that consists only of a head thrown back, smiling eyes, hearted lips, from which no sound is heard. You can read lips for speech, but you can't read a lip for the cause of laughter. It made me lonelier than before. There was vanity on my side, and considerations for me on the other side. They meant to be kind. It was a cruel sort of kindness. Deathness is a progressive thing. It goes downhill. There are days and weeks of improvement, but there are delusions. The progression is down. I decided to go to a famous doctor in Chicago. Mr. Rickman, come here please. Marie, you do hear a little better, don't you? Yes. I'm not as good. It's plain that you should hear better on a noisy screen during a railroad station, but the noise helps, doesn't it? Don't give me him. Oh, don't be absurd, darling. Forgive you for what? For all the crises. Oh, no, I've got it all. Forgive me for making simple things frightful, for making small things oversized, and for making quiet things dramatic. Henry, why am I so frightened? Donnie, I wish I could go with you to Chicago, but maybe it's better for you to do it alone. I'm helping, and your doctor is helping, but, Marie, you have to do it by yourself. The grown people have to do things by themselves. Will you sit down, Mrs. Heiner? The doctor's face was kind. A little brown gnome of a man with a lined face and soft eyes, and a leg that dragged when he walked. We begin, yes? Six, three, two, message. I tried to hear. I tried, yes. Horror, horror, mood. It lasted for hours. This is a monocle. Listen. Now, listen to the buzz. The beast is moist from the dust. He sat facing me, and not speaking for a while. Have you noticed, Mrs. Heiner, that I limp? I am limp. You are hard of hearing. Mrs.  The doctor, I live in a prison. My dear Mrs. Heiner, truth is a healing thing when you are brave enough to accept truth. The truth is that you will never hear any better than you hear now. It will get worse. One foolish people groped in half darkness because they were ashamed to wear eyeglasses. There is no indignity in wearing glasses, and there is no indignity in wearing a hearing aid. Henry and I shopped for a hearing aid. It was as simple as that. Does this sound better, Mrs. Heiner? No, it makes me dizzy. This more comfortable, Mrs. Heiner? No, I don't think so. Tell me if this is better, Mrs. Heiner. One, two, three, four. Better. That is better. Take it home, Mrs. Heiner. Wear it. Try it out. It takes time to get used to it. Don't be impatient. What do you look at if you found a million dollars? I have. Listen. I don't hear a million dollars. Do you hear it? I have to put in a new washer. That dripper driving me. Oh, don't just touch it. Let it drip.  Let the sound alone. I never realized until now how far I'd gone in silence. Let it drip forever. I want to hear it. All right, darling. I'll arrange for all the dogs in the neighborhood to fire. Yes, by all means. And we've got to get a new whistling ticket. Yes, Henry. And wear shoes this week and eat celery and snap your fingers and cough and sneeze and sing and yell. I want every single sound. I sit here again. For a week, a month, almost a year, I was drunk with sound. And then I remembered that there were others. Others who still could not hear, who were afraid, who needed help. All right, call me a woman with a call. I went to the Cleveland Hearing and Speech Center. I began to work with the all deaf, and the half deaf, and the nearly deaf. I worked with deaf children. Mrs. Heiner, this one's name is Betsy. How old is she? She's four. Deaf and dumb. You're new here. When you're around longer, you'll know she can't speak because she's deaf. Hello, Betsy. Hello, Betsy.  Like that. Good. Feel the sound, Betsy. Hello, Betsy. Say it, Betsy. Hello. That's fine, again. Hello. Hello. Good job. She learned. I should have said what I did. You know, well, I just haven't ever thought about deaf children before. I know. Deafness can't be seen. It's invisible. Here, that's it. This is for you. Take it. Good girl. That's it. Take it. Hold it in your hand. Open it. Feel the sound. The deaf are set apart. They withdraw into their own silence. But now they must listen to me because I've got something to tell them. Can you hear me? There are between seven and 15 million Americans who must be made to hear. There are children like little Betsy who are born deaf. They must be taught to speak. There are the old people. They sit in a room and suddenly it seems to them that the last door has closed. There are men and women like me, anxious, afraid, lonely. There are prisoners behind the wall of silence. Seven to 15 million Americans. Listen. I have lately come from where you are. And now I open the Bible to your place. And in that day, shall the deaf hear. Our star, Jean Kearney. There's one thing I would like to be now, not as Marie, but as Jean Kearney. And that is to bring you the real Marie, whose story we told tonight. And here she is, Marie Haley Tiner. Thank you, Miss Kearney. If my experience has helped other people, I am repaid. Today, there are many organizations working among the deafens, particularly the American Hearing Society. Programs like Tonight's Cavalcade and Understanding on the Part of All of Us will help shatter the great wall of silence and imprison so many of our fellow citizens. Good night. Next week, Cavalcade will present one of the screen's most irrepressible personalities, Mickey Rooney. Our play, South of Cape Horn, is the story of a boy who failed to seize to discover a lost potterman. Be sure to join us. Tonight's Cavalcade play, The Wall of Silence, was written by Morton Wichengrad and was adapted from the book, Hearing is Believing by Marie Hayes-Heiner, published by the World Publishing Company. All royalties being turned over to organizations working for the deaf. The program was directed by Arthur Pryor, music composed by Arden Cornwell and conducted by Donald Voorhees. Your announcers, Ted Pearson and Bill Hamilton. Our star, Gene Tierney, appeared to the courtesy of 20th Century Fox and can soon be seen in the Puro Pool. May we remind you when you buy Christmas gifts this year, buy a lot. Thank you. Cavalcade of America comes to you from the stage of the Balasco Theater in New York and is presented by the DuPont Company of Wilmington, Delaware. Makers of better things for better living through chemistry. Stay tuned for The Baby Snook Show followed by Bob Hope on NBC.


Good morning everyone. I feel like I should sing, but I'm not going to sing. I'm going to be talking about blended learning and student protests. And I'm just going to start with two quotes. One of which is that the student protests were described as a meeting of new emerging antagonisms with old resolved ones. These are the student protests in South Africa and Donna Herrera reminding us that technology is not neutral. And I'm going to be talking about how academics in one research intensive university made sense of the role of blended learning during campus shutdowns in 2015 to 2017. In a little bit of context, the South African student enrollments have doubled. Up until 2016, the demographics have changed. The student bodies become much more heterogeneous. But participation and success rates are highly skewed and black students still do much more badly in throughputs in South African higher education. So exclusion takes multiple forms, partly through funding and student debt and the reduction of state funding, but also through the cultures of the universities, especially the traditional research intensive universities. It's impossible to describe the protests in South Africa between 2015 and 2017 in one slide. This was my hardest slide to put together. Any South African who's watching me is going to disagree with my summary. But briefly, there had been protests before 2015 and there are still protests today. But during the roads must fall and fees must fall era, the entire system had protests with universities shut down for days and weeks. There were exam disruptions, delays and postponements. And the logic came to an end when the president of the time announced free education for the poor. There was a huge amount of damage, physical damage to the system up to about 45 million euros. And the protests were about fees falling, outsourcing and transforming the culture of the university. There have been some commentators trying to talk about this. Even the commentators in the books that are being written are highly contested. So let me just clarify that this is an extremely controversial, highly contested era and one that's very difficult to make sense of. But I'm going to give you a little bit of an account from some of the academics. And what happened at the University of Cape Town is that at the end of 2016, which was the second year of the protests at the university, there was an announcement that teaching and learning would resume because the university had been closed through a variety of approaches, including blended learning. This was the first time that academics had heard about it, and it was the first time that the Centre for Teaching and Learning had heard about it when it was announced on the vice chancellor's announcement. So we did a study with four universities who were involved in student protests in different ways. And at the University of Cape Town, we interviewed 16 academics, and they were people who had come to departmental sessions that were run during that protest shutdown period about if you're thinking of using blended learning during the shutdowns, are you interested? So that's how we managed to get those people. It was really difficult because people were very busy and under pressure. And we've actually written about this, drawing on a range of literatures, critical pedagogy, digital colonialism, a little bit about protests and social media, and then some literature on blended learning and challenging circumstances which is less useful because it tends to be about earthquakes or floods where there's much more agreement about the need for blended learning. We used activity theory to map out the account of using blended learning because as I was explaining, it's a really messy and conflicted space, and activity theory gave us a way of mapping the story as told to us by academics, which we found very helpful. And I'm sure many of you are familiar with activity theory. It's really about the subject, which in this case were the academics, and the object which in this case was blended learning towards an outcome which in this case was completing the curriculum for the year and writing exams, which had been under threat because of the shutdowns. And the tools that we used were that we found in these cases were both the protests and political actions and learning technological tools. These were also mediated by the rules of the game, the community this was all happening in and the division of labour. And that is a very detailed summary of what we found that I'm going to run through and which I'll come back to. So in terms of the subject, as I mentioned, these are the academics and all academics were implicated in this decision. So everyone was basically told, encouraged, suggested that they should use blended learning as a way of continuing teaching, but not all of them agreed with this. So whether they agreed, took it on, or didn't take it on, everyone was implicated. And for some people, this was nothing new. So some people said, well, it's already a blended institution. This isn't a big deal. And some of them said, one of them said, my course is sufficiently blended, so moving online is not a big deal. So if you think of a residential university that's in the process of becoming more blended like so many traditional face to face universities, those people are more likely to be at the front end of trying new technologies. But for all of them, it was very emotional and emotive. And some of them were angry, they would say blended learning is a bit of a band aid being stuck over a much more serious problem. In the second and third year, they would say, well, we tried it last year and really there's no appetite for it this year because we had three years of closures. And by the third year, people were actually planning their interventions. And then some people said, I was just so exhausted, we'd be so determined, there'd be no sacrifice. It's tough when you're in the middle of a residential thing and you suddenly have to do everything online. So there was a lot of anxiety and emotion attached to it. And then of course, some people were quite angry about this, where they said, look, blended learning is a deliberate activity and it's not what we're doing. It's got nothing to do with panic throwing things online. It's got nothing to do with what happened at the end of the year.  It's an abomination, okay, to suggest that what we did was blended learning. So that was on the other side of the spectrum. As I mentioned, the mediating tools was the technology itself and people use technology in a whole range of ways. One of the things that people who were already involved in lecture recording did is they carried on lecturing to empty lecture theaters and put the lecture recorded lecture up online for their students. The most common thing really was using the learning management system to put up notes and PowerPoint presentations and so on. But people also used WhatsApp chat groups, voice notes, a number of them made short clips themselves using their phones and some made screencasts. So there was a whole range of users and some people who'd never used technology before came up with various solutions. But while this was happening, all of this wasn't being mediated by the protests and the students who made teaching impossible in a range of ways. And bearing in mind, the student body is not a homogenous group. So you might have student protests, you might have students not protesting. Very, very mixed. But the protests, you ask how is it possible to close down a university? Well, in the one case, as you can see on the image there, if you block the entrance roads, that's a drone image of the blocked entrance road, you can't get onto campus. And then the other way is through disrupting lectures. As in this case where protestors would simply make it impossible for lectures to continue. And then also fire alarms going off continually, which makes it impossible to teach. The other thing that was a mediating factor was that there was security on campus and that was extremely controversial. Most people were very unhappy about security being on campus. So that kind of management intervention had also led to the final exams in the third year being held in a central marquee on the rugby field under a great surveillance, which also made things very tense. So in terms of the rules, what happened is that the primary formal pedagogical rule is for educators to teach face to face. And this new rule that was introduced very suddenly was greeted with resentment and ambivalence.  Or I just felt it was forced on us. There were a number of stakeholders involved. Every single stakeholder within the university community really. And we saw a division of labour between academics who were producing online content, the students who were either receiving or producing it because they also put their own content online. The tutors who played a very important role and the professional staff. So in some cases the tutors had a pens down campaign. They refused to participate. They said it was undermining the protest action. And the Centre for Teaching and Learning found itself in a very tricky situation where as a unit that provides teaching and learning support to the university, however people felt about it, they were actually producing guides on how to do this. And academics said without those professional staff they would have been lost. And people also tried to take into account issues of access and divides. So the central contradiction from an activity theory point of view was that the student protesters were demanding that the academics stop teaching. But the institutional imperative was for the curriculum to be finished and exams to be written. And there was enormous ambivalence about it. People were saying well you have to do what you feel comfortable doing. And at the same time this is not a normal situation. There was a great concern about divides and exclusion. Some people said this is about an exclusionary culture anyway. And the use of blended learning is making things more exclusionary. And others were really concerned about access and cost. And the cost of data for example. And the final thing that people spoke about and which is continued to this day is that blended learning has now developed really negative connotations. So any kind of online and blended learning project there is a danger that in academics minds it's associated with this kind of rough and ready introduction during student protests. So to go back to the image you can see that this was an extremely complex, rapidly changing, very volatile and fragmented set of activities during which the blended learning was introduced. And it really leaves us with the last questions which is what do academics do when they caught in this moral web of choices, compromises, strategies and imperatives about the use of technology? Was the use of technology a betrayal of the fight for free, decolonised education which many academics supported? What was the responsibility of the university to the vast student majority who wanted to finish the curriculum in fact had to finish the curriculum? Was the use of blended learning an appropriate response? And was the use of technology as blended learning even blended learning at all? So I'm throwing these questions out. I wonder what you would have done in the same circumstances given your roles in these kinds of fields as learning technologists and education developers. That's the situation that teachers and learning professionals found themselves in during this era. Thank you. Thank you very much Laura. Are there any questions or comments from the audience here? Thanks Laura. I don't know if this is a question but there's just so many things running through my head and in many ways I can't actually imagine being in that situation. So thank you for sharing that. I think it's really important to us. Just in terms of moving forward, I suppose what you've really highlighted is the danger of technology being imposed. So how do you think or what are the ways that you know of that staff and students are maybe trying to use technology or blended learning or things now in a more positive way? Or is it now just is there always going to be that kind of battle between this was imposed on us so we're not going to do it? I'm just wondering how people are moving forward. They're moving forward in lots of positive ways actually. We have a project that's around blended learning and online education. We have bids and in the bids we actually say this is not blended learning as it was used during the protest era. This is actually intended to improve student learning etc etc and we've got some fabulous projects. We've got a project at the moment on decolonizing African science through a blended format but one has to always deal with that discourse and that set of preconceptions. So I don't think it's closed the door but that's the context in which it's come to exist. And ironically there's been some positive spin-offs that there were some people who had never touched technology who did so during that period and who are now using it which is a really strange silver lining. Thank you very much and I guess that answers the question there a little bit about what is happening now in terms of blended learning. So just another question there Laura. How did you deal with equality issues for students who didn't have access to appropriate equipment? I probably went too fast but we actually developed a guide that looked specifically at issues of inequality and access. The university also provided free tablets and a laptop computer so that students could actually come and get them if they didn't have any. We also gave academics very very short questionnaire so that they could assess the conditions in which they worked. We made a list of all the free wi-fi spots in Cape Town which we shared so we developed a whole range of strategies to try and deal with that and we also tried to keep the university laboratories open which was not always possible. Thank you and I think probably our last question just for this for this section. So was the blended learning that did take place successful in terms of the results? You know the problem with something like this is you can't assess overall you get little flavors and stories and so in some cases yes I think in some cases having access to those lecture recordings and so on was helpful to students. We have also interviewed students as well which we're going to be writing up. The main problem was that the culture in which it happened was so problematic but I think some of those interventions especially things like WhatsApp groups and so on where people kept talking to each other was helpful in some cases in some circumstances to some people. That's great. I think we just actually have got one more question in there and we'll just have time for if you don't mind Lauren. Any lessons for the situation where disruption is caused by staff industrial action? That's not something I have experience of but I would imagine that the circumstances might be different although you do have the the tension between the academics and the senior decision makers and so in this case most academics even the ones who supported the intentions of the protests did want the academic year to finish so although they were resentful about being having the decision imposed on them they weren't actually against the intention of the decision. I think if it's going to be academics who are disagreeing with senior management it's going to be quite different and there the pressure might come from students. That's great thank you very much Lauren that was really insightful thank you very much for presenting and a bit round of applause please for Lauren. Idina's work with learning technologies helps to develop skilled data literate students who can change our world for the better. Teachers and students can develop and share coding skills with multiple our Jupiter notebook servers. Our DigiMap services deliver high quality mapping data for all stages of education. Future developments include a text and data mining service working with satellite data and machine learning and smart campus technology.


For decades, computing became more and more expensive and complex. For 40s, 50s, 60s, IBM, one single company dominated 90% of profitability in computers. And in one single event happened in 1975, PC got invented and barrier to entry went from millions of dollars to thousands of dollars. And as a result of that, many new people could come and play and create solutions that fundamentally change computing. Yahoo, Google, so on and so forth, Facebook, Apple. What is the equivalent of that in public services? What we need to do is bring the barrier to entry down, liberate it, allow many people to come with many solutions, not try to pick the winners, but create the context. And I think in that environment, entrepreneurialism, new ideas, disruptive innovations will flourish. Britain in public services needs to do what Silicon Valley did in technology. What Victorian England did in industrial revolution. We can do that. We've done it in the past. Ask yourself, why is a tiny island like Britain among the world readers in retail, in banking, in professional services? It's because when those things came and telecommunication revolutions came, we overhauled those industries faster than other countries. And as a result, we were in a better sector. Do we do that with our education, with our health, with our public services today? It's our choice and the government shouldn't withdraw from that choice.


Well there are a lot of different painting techniques and tonight in our in focus our cherelle Moore shows us an artist who focuses on one. You've seen watercolor and probably an oil on canvas but did you know you could get all those same effects just by investing in some acrylic paint? Whatever you can create with any other medium you can get the same look with acrylic but it's much easier I think. Pamela Edevold has been painting since she was a little girl. She started doing portraits in high school and never looked back. I love anything with eyes animals people that's the first thing I paint because I like them to look at me or at least be alive while I'm painting. Edevold decided to teach a class on acrylics to let people know how versatile and forgiving the medium can be. Acrylic is was created in the 50s so it's not very old and it's making a lot of progress especially in the last few years it's come a long way so it's really becoming an accepted medium now and you can do so much with it. And it doesn't take much to create a masterpiece. Edevold says you should start with the running faucet then add the three primary paint colors plus white you can even get cheap brushes. You don't want to use your most expensive brushes with acrylics because they they get beat up pretty fast. You don't need to buy a whole lot of mediums or anything to start with you only need water. Once you have your materials then you can get creative. Some of them have beads in them some have glass there's metallics there's all different kinds of looks you can get by using the different mediums you can use use them in collages and to create three-dimensional works so there's a lot of things beyond just the tubes of paint that you can do with them. It's really your imagination is really the one thing that's holding you back. Today the attendees in Edevold's class were taught techniques in making clouds. Next week will be a barn then they'll eventually move on to people and fur. While it's too late to center for this acrylic session other art classes in Bagley can be found on the Bagley Arts Collaborative Facebook page. There's a jewelry class coming up there's a watercolor class and there will be more this fall that that aren't listed yet but there's more coming. Reporting in Bagley with this week's in focus Shromor Lakeland News. If you enjoyed this segment of Lakeland News please consider making a tax-deductible contribution to Lakeland PBS.


What's going on guys? Welcome back to the channel critical overload here So this would be the spoiler free review for spider-man across the spider-verse the sequel to spider-man into the spider-verse now This is directed by Joaquin dos Santos Kent Powers Justin Thompson. It's written by Phil Lord Christopher Miller David Callahan and it's once again star in Chameke Moore as Miles Morales Hailey Stainfield or Steinfeld Brian Tyree Henry Jake Johnson Daniel Kahlua is joining the cast now as well as Oscar Isaac and a few others now This film is revolving around Miles Morales once again, of course after reuniting with Gwen Stacy Miles Brooklyn's full-time friendly neighborhood spider-man is catapulted across the multi-verse where he encounters a team of spider people Charged with protecting its very existence But when the heroes clash on how to handle a new threat Miles finds himself pitted against the other spiders and must redefine What it means to be a hero so he can save the people he loves most now Spider-man across the spider-verse completely surprised me I knew it was going to be good But I just was not prepared for how much more darker in tone this film would be in comparison to its predecessor The writing is miles better. No pun intended there Managing to progress the character arcs for both Miles and Gwen in a very compelling way that examines what it means to be spider-man The impact choices can have on our lives and so much more. So the themes here are dealt with So the themes here are dealt with in a very thought-provoking way that might make this movie a little dull to some younger viewers But everyone else should appreciate the subject matter this type of subject matter being Tackled by an animated movie in this capacity the animation I would say just like its predecessor is simply beautiful if not Again miles better than the first movie and also somehow again Just better all around compared to this into the spider-verse It's a visually stunning piece of art that I would say is just so impressive to watch come to life If you're someone like myself who grew up loving comic books It's just a breathtaking thing to look at each frame just improves upon the last I cannot wait to revisit this movie before beyond drops next year The soundtrack is filled with bops just like the last one which chime in at all the right moments to heighten the emotions felt during certain scenes Daniel Kalu with spider punk is the standout of the variance that we meet. There's a playful Well from the audience perspective you I guess you might find it playful But miles feels threatened by spider punk and their interactions are just hilarious because of this miles is threatened But also inspired by him. So when they're interacting with each other It's a very interesting dynamic that they have being played up during their time together The script digs deeper into the character of Gwen in her relationship with her father And it builds up quite well to showcase how the parental struggles make miles and Gwen the focus of this story And that they are the heart of it all the movie understands that perfectly well and uses it to its advantage As much as I laughed again There's a darker side to this entry that just completely blows into the spider-verse out of the water Miles discovers something no other spider-man has ever had to accept before not to my knowledge anyway And it makes the character that much more easy to root for Shreemik Moore's voice talent is highly impressive here again as well But the bombshell that Miles has to come to terms with is just absolutely Devastating when you think about all the spider-man's that we have fallen in love with before none of them I swear when we learned what we learned It was just like wow how? how refreshing and how dark at the same time, but Shamik's more Shamik Moore is able to capture this Heartbreak but still resilient nature of Miles so well with his voice that it again This new piece of information about his spider origins makes the character that much more Likeable and someone you want to get behind now The news that we learned in comparison to the origin story that into the spider-verse gives us on Miles Also makes his development here that much more impactful in comparison to that origin story The film understands again that Gwen and Miles are its heart and they balance out their arcs effectively to let you know That it's both of their stories this time and not not just miles It's just as much as Gwen's story as it is Miles I do think that the movie went on the tad bit too long But the pacing is fine for the most part besides a couple slow moments in between all the web slinging chaos Yes, there are some cool cameos and there's an even better cliffhanger that did make me a little upset because it was that damn good I cannot wait to see the payoff to that the voice talent is killing it as mentioned Shamik is Incredible at capturing the emotional roller coaster miles and doors during this film Haley Steinfeld is also wonderful as Gwen I love the chemistry between her and Shamik Oscar Isaac, I think it's phenomenal in what he's given to work with and Brian Tyree Brian Tyree Henry is crushing it and Miles's dad who I think is named Jefferson Davis. I'm just drawing a blank I think it's named Jefferson. I just love that relationship unfolding on a screen between Miles and his father in this sequel All in all across the spider-verse is a sequel that successfully builds upon what came before without feeling like a retread besides Exploring the common spider-man things about grief loss acceptance, etc that we have seen in every entry prior There's even a layer of meta commentary I would say in this entry as well that gives a label for these unfortunate events that every spider-man across the multiverse must deal With which I thought was a nice nice touch creatively as well All in all I'm gonna give this movie a 9 out of 10 when you guys see it Hopefully you love it as much as I did and hopefully it's something that many people will look back on and just be very Appreciative of as time passes. This is one of the best spider-man movies to date If you haven't already of course make sure you subscribe turn on post notification in this video in the description I will have links on my social media accounts. I'm on Facebook Twitter and Instagram You can message me there of course them there's any movies news or reviews I'm gonna cover in the future and with all that in mind guys. I will see you in the next video