Welcome to Egan, Minnesota and the Twin Cities Orthopedics Performance Center home of the Minnesota Vikings. This is Titans Camp Rewind. I'm Mike Keith. This is Coach Dave McGinnis and this incredible massive complex, just a little history lesson, used to be the world headquarters of Northwest Airlines. Now it's where the Vikings train and it's easy for them to host another team like the Titans. This facility is unreal. It's so well thought out and everything that you would want as a head football coach or as an organization is right here. Massive footprint and it's very, very impressive. Ideal setup because of the hotel that, you know, the team also owns that's right here for joint practices. Ideal setup, Mike. Titans and the Vikings with a couple of joint practices before the Saturday night preseason game. Coach Mack, just overall, what are the benefits of joint practices for NFL teams? You get, first of all, when you're evaluating players, you want to put them under pressure situations. You've got to find out how they're going to respond to pressure. Sooner or later, you get very, very familiar with working against your own team. This is invaluable, especially now with only three preseason games for your team, the young and your veteran players to work against somebody else in a competitive type situation. It'll be controlled, but the one-on-ones and the team stuff will be very, very competitive. It's invaluable. There will be a lot of tape grinded on this because it's important. These guys are under pressure. They feel it when they come out here. This is why these are so, so beneficial, especially if both teams and both coaching staffs work well together and you get work. You get work rather than just, you know, turning it into, I've been to some of these Mike where it's turned into Braveheart. You don't want that to happen. Coach Dave McGinnis has that to say from Egan, Minnesota. Let's see what the Titans are saying. Bying into what Mike Rable wants us to be in the style of football he wants to have on the team. Seeing how we block different players and seeing how we cover different players and making sure that we're practicing to our standards and our tempo. I thought it was a great day overall for the defense, but you know, we're going to watch the film and find some things to correct. It's great work because we're seeing different looks that we see against our own team on a daily basis and we're going to play teams that they do this type of stuff. So it's good work for us and we'll learn from it. Anytime you get to go against somebody fresh for camp, it's always fun and gives you another boost of energy and it's it allows you to really see where you're at halfway through camp. So you can know what your weaknesses are and what your strengths are heading into the last two weeks of camp to clean them up before we get into the real thing. I think it's definitely big to come out here and start fast, bring our own energy. And I felt like we was able to do that today. It's time to talk about what they're doing at a couple of position groups. Let's talk about the quarterbacks right now as one of our positions of focus today. Ryan Tannehill is off to a great start in this new offense. Coordinator Tim Kelly says it's almost as if Ryan Tannehill created the offense himself. Coach Mack, how can that be? Got a veteran quarterback and and and as we've seen throughout the spring and going into training camp now, there's a there's a lot of motion, a lot of personnel groups with this, a lot of change, a lot of Mike points. There's a lot of things that go on for a veteran quarterback that has experienced a lot throughout his time. This is perfect. It's not overwhelming to him. It's welcoming to him because now he can control the offense and also let's just let me just say this for the first ball game out of the jump, you and I get to see practice every day. Tim Kelly's did a great job of layering the calls on this offense and when I say layer the calls, I'm talking about personnel groups, different looks, setting calls up. I can understand exactly why he would say that but only that can happen with a veteran quarterback. Ryan Tannehill did not play in Chicago. We don't know if he's going to play much in the pre-season game against the Vikings. We certainly will see Malik Willis and Will Levis who did some good things in Chicago and did some bad things in Chicago. A chance now to visit with quarterback coach Charles London to discuss what he's looking for from Willis and Levis. A week of work since you had a chance to see your two quarterbacks play against Chicago. Let's start with Malik Willis. What do you want to see from him against Minnesota? Yeah, I just want to see him to continue to grow from what he did for the first week against Chicago. Continue to command the huddle, speed up our operation a little bit, understand when it's time to go, when it's time to stay in the pocket. I think he did a good job of that in Chicago. Just wanting to continue to grow in those areas. It's interesting with him because a lot of talk from Grant Carthon, from Mike Vrable about hey, we want to see him play quarterback. We want to see him run the show clearly improved in that area, right? Yeah, no doubt. He's got a pretty good grasp of what we're trying to do here. I know he puts in the work, he studies and I just think he's a lot more confident and has a better feel for what we're asking to do and he goes out there and he tries to execute it. Flip to Will Levis. What do you want to see from him against the Vikings? Kind of the same thing from Will. Now he's got his feet wet. He's got his first NFL game experience. Now I expect him to be able to pick up the operation, getting it out of the huddle. Now he understands a little bit more of like what the rush is like in the NFL. So he's not going to have as much time as sometimes he thinks, but I want him to continue to grow. I thought he was decisive in what he was trying to do with his reads, but now with the game under his belt and understanding the speed of the game and what it takes to play quarterback in this level. For both of the quarterbacks, the internal clock and getting that ball out on time, how big is that in pre-season game number two? You know, I think it's huge for both though. That's an area that we've asked him to approve on this week and I expect both of them to take a huge step. You know, there's one time, there's one thing to be able to do it out here in practice when you can't get hit, but then when you got to go out there in the live bullets, everything is going to pick up the pace they've got to pick up and they've got to be able to adjust. The tight end position is also a big area of focus for the Tennessee Titans. Working in the new guys and some veterans who are also new to the system, that's the task for tight end coach Tony Dues. We had the veteran coach wired for sound as we take a look. They're on a line. Here we go. Footwork. Yeah. Breaking them hands with you. Hit. Attack his leverage without losing leverage. This Jeff Simmons out here. Boom. Rock and roll. What up, hey son? Rest the ball.  Get it up. Yep. Make it a habit. Boy, look at here. Stretch them out. All day long. All day long. Why are you sweating like that already? Huh? Let's go. Little ball security. Eyes up. To hit. Don't let it out. Don't let it move. To hit. Eyes up. Eyes up. Eyes up. Oh, that thing loose. Fall back. Fall back. Fall back. Fall back. Let's go. There. That's it. You got to hold the ball tight. You get into it here. Bang it so that when he comes I can get vertical. Be violent with your snaps. Don't be in a hurry to come off on the second level. Be violent in the jig. Work the outside hand. There you go. Come on. Get there. Get the outside hat. Take a level man reach. One of the tight ends that we're watching closely here in Minnesota is rookie Josh Wiley. Fifth round pick out of Cincinnati. Coach Dave McGinnis, your thumbnail on Josh Wiley. Big target. Big tall athlete. Is a smooth runner. Covers a lot of ground. Can eat up stripes. And it's going to be asked to block quite a bit. This is going to be a multiple tight end offense. We've already saw that in the first ball game. Tight ends moving to different spots. Being full backs. Offset strong. Offset weak. Spread out. Split out. This guy is tailor made for this. The blocking aspect of it is something that he will need to improve on. But just a base to work with. Big tall smooth athlete. Very excited to watch him develop. Six seven two hundred forty eight pounder Josh Wiley. Missed some practice time early in camp. Got back to work last week. The preseason game at Chicago didn't go exactly how he wanted. And so he's looking for more Saturday against the Vikings. Josh what are the things that you've been working on during the course of this week? Really it's just like coming together as an offense. Making sure we're all on the same page and doing our assignments. I think that I still have a lot to improve on so just looking to do that a little bit better. How glad are you that the first preseason game is out of the way and now you've done it? Yeah the first preseason game didn't go as well as I planned. Like I said after the game a lot of lessons to be learned. You know it's a whole different ball game and you got to play it to a different standard. The thing is just for having that experience over with. Like kind of like having that hurdle cleared. No matter how it went it's got to feel good. Yeah I mean it feels good but it was also like you know I mean it was exciting for that first game. You know I wasn't looking for it to be over by any means. It was definitely fun. It was really cool. Go play in other color jersey and just looking forward to the next one. How much do you think the work against the Vikings is helping you? I think it's good. You know I think it's always good to see different looks, different people, different bodies. You know they all everybody uses different techniques so it's just good work all around. It's time now to see what we're posting from training camp. On Tuesday before the team left for Minnesota the entire football team and staff took part in the Titans Foundation luncheon at the Grand High. Veteran players sat with guests at each table and enjoyed lunch while the rookies were on stage with Coach Mike Grable being asked to perform a variety of tasks. It was fun for all except maybe for the rookies. The best news nearly four hundred thousand dollars was raised for the Titans Foundation which donates money to worthwhile charities and causes throughout the state of Tennessee. Coach Mac why does Mike Grable think it's important to get the rookies involved in this way? It's essential to assimilate your rookies as quickly as possible into everything and part of being a rookie is not only assimilating into the football part of it but becoming part of the locker room and very very comfortable. And so he is doing this in a way that they feel like they're part of it. They're still rookies but you've got to bring these guys in quickly because you're going to count on quite a few of these guys to be able to help your football team. It's creating that atmosphere where everybody's got a brotherhood in the locker room and when you get them out in public and they do something like this that earns them points with all the vets. Also a chance for you to follow the Titans all of this preseason on all of our socials. We invite you to do that. We have updated coverage and different packages. Interesting interviews every single day. Also invite you to join the latest edition of the OTP. That's the official Titans podcast. You can download it wherever you get your podcast. We'd love for you to rate and review it. Our guest, the voice of the Minnesota Vikings, Paul Allen. I promise it is entertaining.  Titans up against the Vikings. Coach Mac and I will be on Titans Radio starting at 6th Central on all of our great Titans radio stations throughout the Mid-South. For Coach Dave McGinnis, I'm Mike Keith. Thank you for joining us from Minnesota for Titans Camp Review.


Good morning. Good morning. Good afternoon. Good afternoon, ma'am. How are you guys doing? Yeah, we are cool. We are great. Come on. We are cool, ma'am. We are great. Sorry, I thought that was a beauty. Yes, welcome to your session today. Today we will be doing sampling distribution. If you have any question or query, now is the time to ask any question or comment. What we previously did regarding the module, anything? Yeah, assignment two. Oh, Jesus. What's wrong with assignment two? Are you struggling? Yeah, yeah, I'm struggling. I really struggle. But I'm going to do my second attempt tonight. Did you at least watch the recordings and did you do the activities and practice? I've tried, but after tonight I will communicate with you after my second attempt. Okay. Thank you so much. After the second attempt, why can't you communicate with us now during the day when you are still preparing to do your second attempt? So that when you go and do your second attempt, you are sure of what you're going to be doing there. In terms of the activities that we did previously, if you are unable to answer those activities on your own, then it means you need to ask for help so that we can help you understand how to answer those activities. Because if you don't know how to answer the activity, you won't know how to answer the assignment questions as well. So practice now with the activities. Ask questions if you still start. Let's help you.  Okay. Thank you, Liz. I think on assignment two I was not prepared enough and then the time was running out for me. Now that's why I say let me just go through the other activities. And then after my second attempt, I will shout for help. Okay. Of course, assignment one was number one. Assignment two I didn't practice much. Okay. Thank you, Liz. I think I had the same problem in assignment two. When it comes to the theory questions, that got caught me a bit off guard. There were some sections in assignment two where I could fly through because I know how to do the calculations and then it goes back to theory questions and I'm completely lost again. It's also just a matter of watching the videos again. That's why I asked you guys now what videos all covered assignment two. So I was really watching all those videos and doing the activities so that I can do my second attempt. Okay. And then also I get confused with the table sometimes. I just need to focus on that table. Okay. Yeah, especially with the binomial tables and you need to be very careful when you use your binomial table as well in terms of what probability of success they have given you. Whether you must use the left hand side or you must use the right hand side based on the probability that they gave. Yeah, but I believe in if you practice a lot and do more activities. You might master the chapters as well. Do not rush to do the assignment without understanding the concept as well as knowing how to do the calculations. Okay, so let's do sampling distribution. So the last time we met, we discussed normal distribution and the same concepts we learned in the normal distribution. We're going to continue with them today. With normal distribution, we're only looking at one population with sampling distribution. We look at multiple samples that comes from that one sample population as well. We're going to be learning how to use the same table, the normal standardized cumulative standardized normal distribution table that you used in the normal distribution. We're going to learn how to still do the calculation for the Z score to standardize the means and then using the Z score value to go find the probability on the table. So we're still just going to do the same thing that you have learned. So let's get to it. So by the end of the session today, you should learn the concept of sampling distribution. You should also be able to calculate the probabilities relating to the sample mean or calculate the probability relating to the sample proportion. And the sample proportion is another avenue that we are introducing. You've learned how to calculate the Z score using the standard, the normal Z score, which will look almost exactly the same as when we calculate for the sample mean. But we're going to introduce the sample proportion Z score formula as well today. So when we talk about sampling distribution, like I said, with normal distribution, we only look at one population and we estimate or we approximate the observations that we get from there in order to standardize them into a normal distribution. With sampling distribution, it's a distribution of all possible values of a sample statistics given for a given sample size selected from a population. So like I said, in sampling distribution, we're going to use samples selected from that one sample. So in state of using one population, we're going to use multiple samples but selected from the same population. So like example is the one that you see on the slide. We've got three different samples that we selected from this population. And when we calculate the average of those distribution, you can see that the distribution might also be, they might look almost exactly the same but they might be different in terms of how we selected the people that are presented in the sample. And you can see that the mean distribution or the distribution of all the three samples, you can see that they are not actually normally distributed. So with sampling distribution, we're going to take all these sample means and we're going to make sure that we convert them into a normal distribution. So we will take all the samples in average or sample means and standardize them in order for them to be in or to convert them to be normally distributed. So when we talk about the sampling distribution measures like parameters for the sampling distribution. So from a normal distribution, we know that we have a population and we can calculate the mean of that population and we can calculate the standard deviation of that population. And if we do that, for example, if this is our population and it has the values 18, 20, 24, we can see that our distribution will be a uniform distribution. This is not a normally distributed distribution, it's a uniform distribution. So we can take this uniform distribution and convert it to a standardized normal distribution by re-sampling from this same population multiple samples and then use those multiple samples to standardize the distribution. And when we do that, then it means we are doing what we call a sampling distribution. And when we select multiple means from those samples and we calculate the means of those samples, we get that the population mean of that sampling distribution or the sample sizes, all of them. The average mean of those gives us 21. And when we calculate the standard deviation of those, we find that it will give us 1.58. If you look at, if we only had one population, you will notice that we had the mean of 21 and we had the standard deviation of 2.2 from this data set. So if we selected four other samples out of this, so re-sampling the values from this population, we get the sampling mean or the mean of the sampling distribution of 21, which is the same as the mean of the population, and we find the standard deviation of the sampling distribution to be 1.5, which is 1.6, which is less than the population standard deviation. You will notice that we divide each one of them by 16 because we selected four samples.  So that would have been our sample sizes, even though we selected only two samples, but in each sample they were four observations from the normal distribution. So it makes it 16. So in a nutshell, what we're saying is when we have a population with the size of four and we calculate the mean of that population, we get 21 as the mean and the standard deviation of 2.2. If we re-sample and we take two samples from this, from this population of the four individual values from that sample, from that population as it is, but we sample it twice, we calculate the mean of those samples, we find that the mean is 21 and we find that the standard deviation is 1.58. As you can see, we were able to transform a uniform distribution and make it a normal distribution. With the sampling distribution of the mean, if we compare it with the population, we can see that clearly, the mean of a population is the same as the mean of the sampling distribution, but the standard deviation of a population, standard deviation, is not the same as the standard deviation of a sampling distribution and the standard deviation of the sampling distribution is also called the standard error and we're going to learn about that just now. So what we have learned so far is different sample of the same size from the same population will yield the same sample, oh sorry, it will yield the different sample means and also we've learned that a measure of variability in the mean from the sample to the sample is given by the standard deviation of the sampling distribution or what we call the standard error of the mean. So standard error is the same, standard error is also the same as the standard deviation of sampling distribution and it's also denoted by sigma x bar because we're talking about the sample mean so it will be your sigma x bar which is your population standard deviation divided by the square root of your sample. And that is what we call the standard error or the standard deviation of a sampling distribution or the population standard deviation divided by the square root of n and you will need to know this and remember this because in the exam or in your assignment they might be asking questions regarding theory questions and you need to know how to answer that question as well. And the standard error is the same as the standard deviation of a sampling distribution is the same as your population standard deviation divided by the square root of your n. Another thing you need to note is your standard error will decrease when the sample size increases so the bigger the sample size the smaller your standard error will be because we are dividing the population standard deviation with the sample size so if I divide 2 by 8 the value will be less if I divide 2 by 20 it will even be way less so you need to remember that that when you increase the value of your sample size the value of your standard deviation or standard deviation of the sampling distribution of the mean or the standard error will be small let's wrap up what we've learned so far we've learned that the mean of your sampling distribution for the mean is the same as your population mean we also learned that the standard error which is our standard deviation of our sampling distribution of mean is the same or it equals to the population standard deviation divided by the square root of the sample size let's do an example to see if we learnt anything from that suppose a population has the mean of 8 and the standard deviation of 3 suppose a random sample size of n is equals to 36 is selected calculate the mean of a sampling distribution what they are asking you to find is the mean of a sampling distribution what is the mean of the sampling distribution based on the values that we have that is your question am I alone here hello you are not alone you are not alone Lazy okay here is the question what is the mean of a sampling distribution anyone 8 it's equals to 8 because the mean of a sampling distribution is the same as the mean of the population is the same as the mean of a population which is equals to 8 what is the standard deviation of a sampling distribution or what is the standard error 3 3 the standard error will be your population standard deviation divided by the square root of n what is your population standard deviation is 3 what is your sample size square root of 36 therefore this will be 3 divided by 6 which is equals to you can use your calculator and calculate it which is 1 over 2 which is 0,5 and that is your standard error questions if there are no questions then we move on similar to what we do when we calculate the normal distribution we need to standardize the values or the x values or the unit in terms of using the z score or the z value calculation with the sampling distribution we also use the z value to find the standardized value in order for us to be able to go find the probability on the table in the normal distribution our z score was our x observation minus the mean divide by the population standard deviation and that is what we use in chapter let's say study unit 6 in study unit 6 in study unit 7 we use the sample means instead of using the x we're going to use the mean so we're going to say it is the mean sample mean minus we're also not going to refer to the population mean but we're going to refer to it as the mean of the sampling distribution because we're using the means divided by the standard error which we know for sure it is your standard deviation divided by the square root of n so this formula is to standardize our sample means in order for us to be able to use the standardized units to go find the probability on the table and the formula we can write it as your mean bar minus your mean because we know that the population mean is the same as the mean of a sampling distribution so we can just write x bar minus mu divided by the standard deviation divided by the square root of n let's look at the next example suppose a population has the mean of 8 and the standard deviation of 3 suppose a random sample size of n is equal to 36 is selected what is the probability that the sample mean is between 7.8 and 8.2 same we know we want to calculate the probability and here we have the sample mean but it lies between remember we don't have to worry about the greater than an equal or less than an equal because we know we're using the cumulative standardized normal distribution so this will be 7.8 and this side will be 8.2 and that is what we need to be calculating so to calculate this probability we need to standardize the mean distribution and standardizing the mean distribution means we're going to use the formula our mean bar minus the mean divided by the standard error which is the population standard deviation divided by the square root of n change to the z because we are standardizing the mean bar minus the mean divided by standard deviation divided by the square root of n substituting the values in terms of what we are given we are given the mean we are given the n we are given the standard deviation and we are given the sample mean in terms of the question so our sample mean for the first one will be 7.8 minus our population mean of 8 divided by our standard error which is 3 divided by the square root of 36 same this side our sample mean is 8.2 minus our mean of 8 divided by our standard error which is 3 divided by the square root of 36 so now we can calculate the side we know the bottom part because we did calculate the sample standard sampling distribution standard deviation and we did calculate it we said it sorry we said it was 3 divided by the square root of 36 and we found that it was 0.5 remember when we were doing the activity found that it was 0.5 so therefore this will be the probability of 7.8 minus 8 will be 0.2 divided by 0.5 you can just double check my values and minus miss list minus 0.2 yes minus 0.2 and then this 8.2 minus 8 is 0.2 divided by 0.5 and therefore the probability that we need to find will be 0.2 minus 0.2 divided by 0.5 what do you get do the calculation for me minus 0.4 0.4 and I'm going to put 0 there because we always need to leave our values into 2 decimals greater than Z and therefore this side will be 0.40 as well 0.5 so now we have the probability of between and since this is the probability of between we need to say this will be the probability of the why am I dividing by 0.5 again here we say we will find the probability on the table for 0.40 minus the probability we find on the table for Z less than minus 0. for Z minus 0.40 so we're going to go to the table let's go to the table let's keep everything that we have go to the table we're looking for 2 values the first value we're looking for it's on the positive side of the table we're looking for that 0.40 at the top we find that that is 0. 0.554 Iron out of base so I'm going to write it here 0.5 4 and then we're going to subtract go and find minus 0.4 on the table we go to the negative side of the table and go look for 0 minus 0 and I know that this column is 0 at the top there for that we'll see so roll up and you will see that that is 0.0 and then you come down to that column and we get 0.3446 0.3446 minus 0.3446 and if you do the calculation what do you get? Miss Liz can I ask a question before you continue? Yes. Why are we using 0 and where does the minus for both of them? Why do we subtract instead of adding what is the reason for it? Let me take it back remember when we use the normal distribution table probability of Z less than a value it will be the value we find on the table remember that? Yes I do. And when we have the probability of Z greater than a value we say 1 minus the value we find on the table. Oh okay yeah thank you so much for that. Then for the probability of between if it lies between A we say we take the probability of the second value which is Z less than B and we subtract the probability of the first value which will be Z less than A and it's the same so the value of table value of B minus the table value of A. That's what we're doing because it was in between we take the table value of B which this side will be B this is A and this is B. So we take the table value of B table value of B which is the probability we're going to find for B subtract the value we will find for the table value for A which is minus 0.4 What do you get when you calculate? Okay since you guys you don't want to talk to me 0.3108 0.3108 and you can see that we took the population distribution that we had we converted into a sampling distribution and then we went and found the probability of that normal distribution which now is standardized Miss Liz going back to the table can you please go to the table why do we use the first column 0? Is it always going to be 0 if it's in B? No. You asked the question why we using so the question the z's go actually with 0 comma for 0 remember the first the one before comma and the one after comma we always find it oh yes the second one the last digit we find it at the top so at the top that is why you always need to leave your answer at 2 decimals oops oops oops that is why you need to always leave your answer into 2 decimals so that the last digit the last digit will tell you in which column you need to be at the first two digits the one before the comma and the one after the comma will tell you which row you need to be at okay Thank you so much Miss Liz No worries let's do an exercise this is your exercise to do a sample of N16 observation is drawn from a normal population with the mean of a thousand and a population standard deviation of 200 calculate the probability that the sample mean is less than at 1050 remember the formula for z z is the sample mean minus the population mean divided by the standard error the sample mean you are given in the question the standard deviation the N and the mean are in the statement you have 5 minutes and your time starts now remember when you have your answer you can post it on the chat are we winning? Yes Miss Liz I'm unable to type on the chat can I share my answer? Yeah when we get there when we get to are we done? anyone still need more time? okay violence means you are all done so we need to take that probability of the mean less than 10,000 150 and standardize it I'm just going to use the same formula and you guys need to tell me what you did so give me the values what is our mean sample mean is 1050 1000 and our population mean is 1000 divided by our standard error it's 200 200 for the population for the deviation 10 by the speed of 16 10 divided by the speed of 16 1050 minus 1000 gives us 50 divided by our standard error is how much? it's 50 divided by 50 that is 200 divided by speed of 16 is 200 divided by 4 that is 50 and then 50 divided by 50 so that will be 50 divided by 50 so the standard error is 50 and we need to go find the probability that such is less than 50 divided by 50 is 100 so we are looking for the probability of a less than 100 so we need to go to the positive side so we go to the positive side of the table and we need to go to where it is 1 because we are looking for 100 0 so 1 from 0 and 0 at the top and the answer is 0,8 0,8 0,8 0,8 0,8 0,8 0,8 0,8 0,8 so I didn't go to the table that I'm not looking for the net. The minute that ask you to find the probability you must always make sure that you go to the table so you need to always feel you I'm not sure how you did it Lady where you got 0,538 but I hope you know where Can you please show me the table again? The table is the cumulative standardized normal distribution. You need to look for 1 comma 0. Oh, I see you went to 0 comma 1. You need to go to 1. Remember, the digit before the comma is 1. So you need to go 1. And then the digit after comma is 0. You need to go to 0, 1 comma 0, and 0 at the top, the last digit 0, and that is that. So I can see you used that. Yeah, that's exactly what I did. I used the wrong value before the comma. Yes, so you need to pay attention to your values. Right, otherwise you do understand how to use the table. Just pay attention to the decimals and the values. All right, let's continue. Now let's look at how we do for the proportion. So far we've learned the sampling distribution for the mean. How do I know which one I'm working with? As long as they mention the mean, the standard deviation, you must know that you were working with sampling distribution sampling distribution of the mean. And to know that is if they give you things like the mean, the standard deviation, you should know that. Because you can also find the sampling distribution for the population proportions. And with the population proportion, we use the pi, which we used in the binomial distribution as our probability of success. Here we use it and we call it the proportion. Population proportion. For sample proportion, we use or it's denoted by a pi. Remember always for the population, we always use the Greek letters. For the sample, we always use the English letters that we always know, like the small letters like p's and the x and the n. With the proportion or parameters, we use the Greek letters like mu, sigma, pi, which is one of those. So for example, sometimes when we calculate the sampling distribution of our proportion, they might not give us the sample proportion, but they might give us the observation satisfying that sampling proportion or the sample size. And when they give us those observations that satisfy that sample, we can calculate the sample proportion because we're going to take the sample or the observation and divide them by the sample mean in order for us to calculate the sampling or the sample proportion. And always remember, your probability should always be between 0 and 1. The same thing that goes with the sample proportion. It's always going to be between 0 and 1. And with this, we always assume that when we do the sampling distribution as well as with the mean, we always assume that the sampling that has been done is with replacement or without replacement. With replacement, it means when we take out one, we create the first sample and then we take them back.  And then we re-sample again, and we take them back. When we do without replacement, when we take out the first sample, we don't have to replace everything that we took out. So we are left with whatever we are left with. And then we go back and we select another sample from what we left with. So it's different. So with replacement, it means if I have all these dots, if I take this dot out and that dot out, and I create a sample, I must take them back. I must take them back and then recreate another sample, and that can be out, and that can be out. And then I must take them back and create another sample. Without replacement, if I have those dots, if I take out this one and I take out that one, I've taken them out. I don't have to replace them again. So they are gone from the sample. So it means they are gone for the next sample. Then when I create another sample, I just select that one and then select that one. Then they will be gone out. I cannot re-select them again. But with this one, I must put them back because they can be eligible for being selected again and again and again and again and again because I'm replacing them again. And that is without or with replacement. And that's what it means. It means the samples that we create, they can either be without or with replacement. Okay, similar to what we did with the sample mean, sampling distribution as well, we can approximate it to a normal distribution when our sample size multiplying by the population proportion should be greater than five. And our sample size times one minus the population proportion should also be greater than five. Our sampling distribution is distributed with the mean of the sampling distribution of the proportion, which is equals to our population proportion of sampling distribution, which is the same as the pi, and our standard error, which is our standard deviation of our sampling distribution of our proportion. It's given by the square root of your population proportion times one minus the population proportion divided by n. For sampling distribution, the mean of a sampling distribution is the same as the pi, which is the population proportion. The mean of a sampling distribution is the same as the population proportion, which is the pi. The mean of a sampling distribution is the same as the population proportion. The standard deviation of a sampling distribution, which is also called the standard error of the sampling distribution is given by the square root of your population proportion times one minus the population proportion divided by the sample size. Let's look at an example. From the past knowledge, Africa check knows that the true proportion of ghost profiles on Facebook is 0.2. There we are given our population proportion. Suppose that we take a sample of 200, which is our end Facebook profile, and we found that only 34, which is our X because this is from our sample of 200. We found that our only 34 of the ghost profiles. What is the value of your population proportion? The population proportion is given in the question. Our population proportion is 0.2. What is the value of our sample proportion? Remember, if we are not given the sample proportion, but we are given the observations that satisfies that sample divided by n will give us the sample proportion. What is the sample proportion? Our observations, they are 34. Our sample size is 200. Therefore, divided by 200 is how much? 0.17. 0.17. Population proportion, yes, it's correct. No, it's not correct. Not correct, not correct. This is the value for the sample proportion. This is the value for the population proportion. Population proportion is 0.2, correct. Sample proportion is 0.17, correct. That's not correct, that's not correct. Option number four, the answer you were looking for. Any questions? If there are no questions, then let's look at how we calculate the Z-score and go find the probability on the table. With the proportions to standardize the value of our sample proportion, we use the Z-value formula, which is our sample proportion minus the population proportion divided by the standard error, and we know our standard error is the square root of our population proportion times one minus the population proportion divided by n. This is for the proportions. If the population proportion is 0.4, our n is 200. What is the probability that our sample proportion lies between 0.4 and 0.45? We can go and find this probability. I'm going to use the Z-score without using the probability of between-between, we can substitute them later in the formula because I'm going to run out of space if I do that. I'm going to first calculate the Z for the first one. We know that we use P minus the population proportion divided by the standard error, which is the population proportion, one minus the population proportion divided by n. I calculate for the first one, our sample proportion is 0.40 because it's given in the question. Our population proportion was given in the statement, which is 0.4 divided by the square root of 0.4 times one minus 0.4 divided by our n, 200 equals 0.40 minus 0.40 divided by the other value, which I'm not going to even bother doing because I know 0.4 minus 0.4, any value divided by 0 will just be 0. I'm just going to leave it as 0.00. Then we do the second one, we'll do the second one, Z equals our P minus the population proportion divided by the square root of our population proportion, one minus the population proportion divided by n. 0.45 is our P because it's given in the question, minus 0.4 divided by our standard error, which is 0.4 times one minus 0.4 divided by 200. Now I need your help because on the first one, I could have went and calculated the standard error, but I was so lazy because I know that the first one is 0. Any number divided by 0 will just be 0. On this one, we will need to calculate it together. 0.45 minus 0.4, the answer here will be 0.055. Please go and calculate for me, the standard error. This will be 0.4 times 0.6 divided by 200. If you quickly do that calculation for me, and then take the square root of the answer. 0.034. 0.034. Then divide 0.05 with 0.034. Is 0.034 the answer for the whole thing or are you? No, no, it's the only number that's about 0.1. Okay. So do the 0.05 divided by 0.034? It's 1.470. You guys, I'm going to rely on my slide now. 0.034, yes. So that is 1.470. So we leave it to two decimals, so it's just going to be 1.47. Now, let's calculate the probability. So we know what we need to be calculating here. So we need to find the probability of Z. Z lies between two values. It lies between 0.00 and 1.47. So we need to go find the probability that Z is less than 1.47 on the positive side, and we also need to go find the probability that Z is less than 0.00 on the positive side. So let's go to the table and I keep going to the table. We're looking on the positive side for two values, 1.47 and 0.00. 0.500. We need 1.47, 1.4, and we need to go find 7, which is 0.9292. 0.9292 minus 0.500, and that gives us 0.4292 and that is how you go find the probability on the table. So, Lizzie, can you please go back to the table, find that value again and just want to see something. 1.47, 1.4 on the side, and at the top we go look for 7. Okay. Thank you so much. And for the 0, 0 and 0. Thank you, Lizzie. Okay. So we calculated the standard error and then we calculated the probability and we did find that it is so you guys, you told me it was 0.147, it's 1.44. So depending on how many decimals you kept, so always keep it to four decimals. Don't round off quickly because you see when you round off quickly, you're adding up values as well. So please pay attention to how you round off. So do not round off, what does the golden rule?  So we rounded off the standard error to 0.34. Actually it should have been 0.35. So you said it's 0.34, so you also didn't round it correctly. So because we are rounding off too quickly, we're adding up there the digits at the end and that is why the answer we got there was 0.47 instead of 1.44. This is what is going to happen in your exam or your assignment while you are busy. Always, if you want to shorten the value you see on your calculator, keep it to four decimals or five decimals, there should be enough to cover the loss of the last digits every time, or the incrementals of the last digits. That concludes what we needed to learn about the sampling distribution. In the next couple of minutes that are the next couple of hours that we have, we're going to do a lot of other exercises that talks to the sampling distribution as well. Then I send you guys an announcement via my UNISA. So next week, Wednesday, there's no class because it's a public holiday. The following weekend, which is Saturday, next week, Saturday, we are going to repeat chapter six and chapter seven activities. So that we can be well acquainted with the two chapters before you do your assignment three, because it's due on the date yet. We still have enough time so that you can do a lot of practice before you submit your assignment three. So we will discuss the activities on Saturday. Do you have any query before we start with a lot of exercise? But before your queries and questions, let's answer this question. Then I think after this, we can start with the questions. Just to familiarize ourselves again with the proportion. Now, remember with the mean, with the sampling distribution of the mean. Remember that the key thing that you need to remember, when you see or when you read the question is, things like the mean, the standard deviation. Say with the sampling distribution for the proportion, the key thing here will be, they will tell you proportion, they might give you decimal or they might give you percentages. So you need to know those things. They will not mention the mean or the standard deviation. So you need to automatically know that this is a sampling distribution of the mean, sorry, of the proportion. For example, yeah, from the past, knowledge Africa check shows that the true proportion of ghost profiles on Facebook is 0.2. The sample size is 200 and they found that only thing for our ghost profile. If the population proportion is 0.2, the sample proportion is 0.17, what is the probability of that? The sample proportion being greater than or at least 0.7. So they're asking you to find the probability that such is greater than the sample mean minus the mean divided by the standard. No, they are not asking you that. Why? Because this is for the sample mean. They are asking you to find the sample proportion minus the population proportion divided by the standard error, which is your population proportion 1 minus the population proportion divided by n. You need to know the formula as well, which one to use for which question, whether for the mean or for the proportion. That is your exercise. You have five minutes. We did calculate the proportion. Yes, and yet they've given it to you. So find the probability that it is greater than 0.17. Your five minutes starts now. Remember those who are done, you can post your answer on the chat. Okay, how are we doing? Are we done? Okay, so let's work it out. What is the probability? The proportion will be? I got option 1, 0.8554. Yeah, but let's work it out. Our p is 0.17 minus our population proportion. We were given 0.2 divided by our standard error, which is the square root of our population proportion, which is 0.2 times 1 minus 0.2 divided by our n. 200, sorry, 0.17 minus 0.2 minus 0.03, our standard error, 0.028384, 0.028284. Did I write it correctly? It's 0.2, there's no 0 after the other 0, after the call. What? Is it 0.028284? No, 0.028284. Did you guys calculate this? Adidas, do you agree with Laleigh? Yes, it's 0.028284, correct? I agree, then we can move. So what is the answer? Minus 0.03 divided by 0.028234 is? 1.0638. Minus 1.0638. Am I right? I think I will check something. So, Lizzie, why don't you check? Those who got the answer, someone gave me the answer and they said it's 0.8554. What was your z value? 1 was 1.06066. OK, just need to round it off, but yeah. What happened to the minus? It's minus 1.06067. Is it 1 rounded off to 2 decimal? Give me only 2 decimal. Yes, that's right. 0? Minus 1.06. OK, so if we go to the table, we must remember that. Why did I tend the sign? The sign must be greater than. Yeah, I was actually about to ask, but OK. The sign must be greater than, so we must go find the value on the table and say 1 minus the value we're going to find on the table under the z of less than minus 1.06. That will be the value. So let's go to the table. We're going to the negative side and we're looking for minus. 1.06, that's what you told me. 1.0, and I must go to the top to look for where 6 is. 6 is in this column. So where they both meet, 0.1446. Therefore, the answer here we find will be 1 minus 0. I forgot the number. 446, 1, 446. 1, 446. And when you calculate this, what do you get? Is that the answer? Yes, 0.8554. And that's how you will find the probability of the sample proportion greater than 0.16. OK, let's fit in one more exercise. Any questions? Nope. OK, we will do a couple of exercises. We have 30 minutes. The standard deviation of a sampling distribution of the mean is called sampling mean. Is it called residual? Is it called standard error? Is it called standard normal? Is it called sum of deviation? What is the standard deviation of something? Isn't it the standard error missus? It is indeed the standard error. Let's go through its statement and choose the one that is incorrect. The mean of a sampling distribution of the mean equal to the population mean. The mean of a population distribution is the same as the population mean. That's correct. The set score of a sampling distribution of the mean is equal to the difference between the sample mean and the population mean divided by the standard error divided by the square root of the sample size. If I rewrite this, it says our z is the sample mean minus the population mean divided by the standard error divided by the square root of n. Is that correct? Yes, that's correct. Is that correct? Because standard error, remember what the standard error is, is the population divided by the square root of n. So are you telling me that this, what they are saying is the mean minus the mean divided by population divided by the square root of n divided by the square root of n. That's what they are saying. Is that correct? Because the standard error, remember the standard error is the value underneath the, is the population standard deviation divided by the square root of n, which is our standard error for the z formula. Take number two, it says the z value is the mean minus, the sample mean minus the mean divided by the standard error divided by the square root of n, which means they are saying is the sample mean minus the population mean divided by the population standard deviation divided by the square root of n divided by the square root of n. That's what they are saying. That is incorrect. That is incorrect. The next one, it says the standard deviation of a sampling mean is equals to the standard deviation of the standard of the population divided by the square root of n. So what they are saying is the standard deviation of a sampling distribution of mean is the same as the population standard deviation divided by the square root of n. Is that correct? Correct. That is correct. Number four, a sampling error is the error resulting from using a sample characteristics to estimate the population characteristic. Is that correct? I'm not sure. From chapter one, what did we learn? There are two types of statistics. There is one, where we use descriptive and where we use the inferential. And we also learned that we use statistics to estimate the parameter, isn't it? A sampling error is one of the values we use because this comes from a sampling distribution. Remember that it's all the samples, samples, samples, samples. The standard error from there will be the error resulting from our statistics, which are our sample characteristics to estimate their population parameter, which is our population parameter, whichever one we use, whether we use the population proportion or we use the population mean. So this is also correct. So this goes back to, if you still remember what you've learned in your chapter one, you still can apply that concept here. Number five, regardless of the shape of the distribution, the sample size gets larger enough. The sampling distribution of the mean is approximately normally distributed. So regardless, if we have a uniform distribution, if we increase and we create a lot of sample sizes, we can approximate that to a normal distribution. Is that correct? We've learned this just a couple of minutes ago. Yeah, yes, yes, that's correct. That's correct. The only thing that is incorrect is number two. That is your exercise. Suppose Africa check conducted best research using a sample size, which means our N is 100. The number of times an AI algorithm is successful and detecting fake news is normally distributed with the mean of 900 and the standard deviation of 100. Let X be or X bar be the number of times the algorithm is successful detecting the fake news. What is the mean of the sampling distribution of the mean? I think the answer's in the question 900. The answer is 900 because we know that the mean of a sampling distribution is the same as the mean of the population which is the same as 900. Number four, you can see what is the standard error. They're asking you to find the standard error and I'm just gonna give you the formula for the standard error. What is the standard error of the mean? It's 100, it's the same as standard deviation. Nope, it's not the same as the standard deviation. You have the formula there, did you calculate? Remember that your standard error of the mean is your population standard deviation divided by the square root of N. Is it number four? Okay, I've got two answers. Let's calculate. What is our standard deviation? 10, 10. 100, 100. Right, square root of 100. 100, 100. So this will be 100 divided by 10. 10. 100 divided by 100. So which is equals to? 10. Which is option? You must use your calculators guys. You must calculate. When they ask you the standard error, you need to know that it is your population standard deviation divided by the square root of N. And you must substitute the correct values and do the right calculations. Okay, now calculate the probability that the mean is less than 920. So you need to find the probability that z is less than your mean minus the population mean divided by the standard error. You've calculated the standard error of this question. It's here. So you can just substitute the values. So we can just say the probability that we're looking for z less than our sample mean is always asked in the question, which is 920 minus our population mean, which is 900, divided by our standard error. We've calculated it. I'm not going to substitute the values again. I'm just going to put the 10 and do the calculations, which is 20 divided by 10. Which will be z alpha, what is 20 divided by 10? Two. It will be 2 comma 00. And then you go to the table and go find 2 comma 00. Go to the table. Go to the positive side of the table. And we look for two. And what is the answer? 0.9772. And it means it's none of this. And the answer here is, that's what happens with the copy and paste. The probability is 0.9772. And that should be your last, last, last, last exercise that you do. Actually, let's not do that one. Let's do this exercise seven. In a random sample of 100 people, 25 are classified as a meeting classified as meeting a characteristics of interest. That is success. Suppose the proportion of success is known to be 0.3. What are you given? Let's first identify what you are given. What is 100? N. 100 is N. What is 25? X. 25 is X. What is 0.3? Pi. Population proportion. So based on what you know that you are given, we know that this is the population proportion question because it's also guided by those key words that you can use. There is no mean, there is no standard deviation. The question says what is the sample proportion? Sample proportion X divided by N. You just need to calculate that. The next one it says what is the standard error? Your standard error for the proportions. The square root of your population proportion 1 minus the population proportion divided by N. What is the number? It's option 4. It's option 4. So let's do this. Sample proportion X is 25. Divide by our N. 25 divided by 100. 0.25. 0.25. Sampling the standard error. Standard error is 0.3. Our population proportion is 0.3 times 1 minus 0.3 divided by 100. And the answer we get is 0.0458. 0.0458. Happy? Yes. Okay. So you have additional exercise that you can do on your own. Remember we didn't cover exercise 6. So you must do exercise 6. Exercise 8. Exercise 9. Exercise 10. 11, 12, 13, 14, 15, 16, 17. On your own. And then next week Saturday we can also do some of those activities as well in class. I will add them to the pack of activities that we will do next week. The first hour we will dedicate it to chapter 6. And then the next hour we will dedicate it to chapter 7. Just to recap on what we did today. You have learned the sampling distribution. You have learned how to calculate the probability of a sampling distribution for D. When you are given the mean standard deviation and the sample size. And you are also able to calculate the probability of a sampling distribution of a proportion. When you are given the population proportion and the sample size and the sample proportion. And in case where you are not given the sample proportion. You are given the observations that satisfy that sample proportion and you can calculate the sample proportion. And we've learned how to look for the probabilities on the table. With that it concludes today's session. Any question? How are you feeling? Any comment that you want to share with the rest of the class? Honestly I keep forgetting the square root and it's giving me wrong answers. Guys please don't do what I'm doing. Thank you. That's a good advice. Just to comment. I think initially when you had mentioned that we are changing uniform distribution to standardize it. Initially it looked like perhaps we cook in the books. But I think now I'm getting the idea that actually what we're doing is we are looking closer into the data that's presented to us. And then give and then change it into a form that's easier to understand. Is that a correct way of thinking? Not necessarily. We converted to a form that we can make conclusions about the information. Because you cannot interpret a standardized value. You can interpret it but I mean like when we talk about the Z score of minus 1.5 or let's say that. Then we're talking about how the difference. We're talking about how far apart the values are one another in terms of the Z score. We're talking about the average of those values. So because we're standardizing it, it's not in the original value. But it is in a standardized form. So yeah. So we're not also actually cooking the books. We're converting them in order for us to be able to make conclusions about that information. Because usually you cannot, when you have the sample values, remember you selected them from a population. And whatever calculations that you do and whatever conclusion that you want to reach it. If your data is not normally distribution, you cannot infer your results back to the population. We cannot make a generalized statement about the population. So only when your data is normally distributed.  And what we are doing. We're trying to make sure that whatever the conclusion that you will reach using the values that you have. You can generalize it back to the original population. Okay. All right. Thank you ma'am. No worries. Okay. And that concludes today's session. You can have a lovely weekend. I will stop the recording and see you on Saturday.


Hello everybody, Andrew Majeski here with Dental L. So let's talk about the board exam. You might have been studying like crazy for the past little bit and you're at the point where you just don't know what else to study and or you just want to do whatever you can to pass that exam. You're at a loss. You feel you have looked through everything. So the best thing to do, you guys, is not to give up now. Still study every day. That's so important, but mix up your studies. Sorry guys, my crazy dog. See the males here. Nope, just somebody walked on a sidewalk. Anyways, sorry guys. So studying can be different for everybody, meaning if you're that person who likes to go through the textbook and highlight all of your notes and that's the way you study. Okay, great. But mix it up now. Go over mock exams. Just do a bunch of mock exams. If you're with a bunch of students, I guess doing your like study clubs, group sessions, maybe everybody can make a mock exam on a different topic and then share it with everybody.  If you're sick and tired of looking at them, but who is ever sick and tired of mock exams, then just look at our session recordings. So if you are a student of mine, we meet online once a week, sometimes more, a full hour of just mock exam questions where we just go through different questions. Different topics per week and that can really help to get things moving. And so you really know what you might need to study further. Like this week we are going over anatomy. So just mock exam questions on anatomy. To see if you really do know anatomy. So, but if you're not a student of mine, that's okay. You can still study it up. So if you have been looking at mock exams, but I suggest just opening up your textbook. Reading a couple chapters today, a couple chapters tomorrow and study that way. If you have been doing that, then mix it up again and look through your notes from school and just study that way. The worst thing you can do is to only study what you think you don't know. So as silly as that sounds. Don't only study things you don't know. Study again things you do know. Like you might be thinking, oh, I know all about teeth stains. I don't need to study that again. Well, you probably do. Read through that chapter and there will be something new that you will pick up. Trust me. There's always something new. So don't be afraid to keep on studying. Mix it up and don't be afraid to study what Sorry for my crazy dogs. You guys. That's what happens when you work from home. I will talk to you soon. If you need anything, please let me know. I am so happy to help and I'll see you guys in the next one.


Hello Then we talk and welcome questions and Comments, so feel free Go ahead So distributing secrets my talk is a little bit about a problem possible solution with distributing secrets in networks So what happened? Historical secrets were used Usually what happens is that This isn't a secret doesn't mean giving passives to users. That was the simple Or all monolithic applications even over networks. You have just that one server that one password That was it Very simple There isn't much to distribute except for giving our passive users But then it wasn't an ethical problem was like interaction Then containers cave But Distribute system cage and distributed system and containers are like distributed system to the maximum. So Let's see what happened. What happened is that now They're not just going to one single place one single password is something now people are using directly or through devices like Biphone's other services that use other services use other services that talk to other things And most of the things to somehow authenticate each other because they run on a network And sometimes maybe the errors within that first you can kind of trust Maybe we need a single machine to have connections that are not authenticated or maybe even not encrypted but in most cases you cannot assume that you have to actually Add credentials Maybe even certificates when you want to do tls connections and all I don't know keys for s3 or whatever other Clusters you have there are a bunch of Things you know secrets everywhere in any distributed system so How do people tend to address this problem in the real mystical system? Like a micro services with a bunch of containers running all over and services they use Provisioning systems Is nice big centralized systems They hold the configurations and on the side all passwords in the clear All the admins that do anything in this mysterious system has access to this data And they just get distributed immediately to all the hostile containers Some people go to the great steps of vacancy So the images and then publishing them and they find out oh all my house and keys are there What happened? Why am I I can't try a thousand dollars? Or maybe in The opposite is Which is also bad because if you remove the password accidentally you get a deeper repository It's still there because it just passed it out, but the previous patch is still in their position. So it's kind of Interesting Thing and if you're doing that, yeah, you're doing something wrong Hold me your wish earlier. Give me four things you do and I'll find five things. You're doing wrong But I secured one of you so We're all the same though The main thing I think people need to really realize especially infrastructure Is that secrets are not Sure, secrets are kind of configured in applications very often But they are not configuration. Most of the case of configuration can almost be public There shouldn't be much in your configuration files That really compromises you critically in that experience except for secrets, which are in your configuration So Maybe there is a better way And I don't know if you'll agree. Maybe you think there won't be a little bit for that So let's try to define a little bit of problem space and if anybody speaks in audio or watch the video Don't worry about it It's not bad So I find things I I kind of Um Find out that are really interesting When they take a problem how you distribute all these secrets you have around they have to manage And on how to provide the secrets update them preserve them protect them and finally out of them So the next few slides that two statements about every any of these problems and one is What happens in traditional provisioning systems is used to distribute this information And what happened if you weren't using API? So provide a secret what does it mean? So you get a secret from application and need to private it So you have a bunch of containers that need to access Remote files system how do I give it credentials? All the classic provisioning system will just have this Usual password or a key In a static file, which is pushed to the machine Uh in the API world What happens is that if you can you make the application actually pull the secret When they or you have a helper at least opposing when you start a good thing. You don't Bang this security in the browser system Update what does it mean? Well Bracers may be compromised and I have to change them. You know I might have to rotate them So in the traditional provisioning Or what you can do is to change the configuration at some point and then push out new configuration and probably wish to have a service You know to make it great this new secret music With an API you can have notifications or have application actually pull it when it's ready And that may be even restarting the application itself just start using the music Preserve So this this is something that affects mostly the container world I think in the container world you have images, but when you're having to do updates What you do is that you just wipe the image and you belong to a new one And you have the problem The data you have to preserve part of this data usually is pass or pass out the service because yes You want that data software, but you want to just keep collecting to that database and so Again, you need to have a way To either preserve these credentials in a way that when the container just started they are still there Or you need to inject them And you know to clear what happens when the region system is not involved it can just start new images already low Again the naked case you just let the application pull it so you don't care How you update a private preserve is there it's in the It's in the service that hands out the secrets and the application just know how to pull it Protect So how do you leave an access to the secrets and one of the big issues I see at least in the Provisioning system is that you have this all this bunch of signal for all these applications And the provisioning system uses a man space that's a group of people That means this group of people have access to all the credentials for all the applications Even though they are not necessarily Managed the application. Maybe they just provide the service to push coffee or a shower Uh in an IP world An IP world is that what you can do is that you can have access control So you need specific secrets maybe database secrets only to people that manage the database or only to the application At that specific data lines. These things are not all Accessible at the same time at the same place placing people. You don't have to have people get it right What if someone sends a brown configuration to a brown server? You don't have to worry that much about their names And find an audience So how do I know The secret of not being compromised in a traditional Case where we just have to you know, something that is used to push configuration you have to audit I don't know everything I've seen I don't nfs I mean, yeah That's been possible actually to retrofit that Auditing in such a system so that you can track who has seen this secret going on In the native care world much easier You will have one service that has a password knows What a knows what application is trying to pull it That's when you can trap that much more easily because you have just two points The place where there's two or in the place that asking for the last you don't have all the other infrastructure in the middle It's not for service secrets But Wait, I've been talking about ipi, right? How do I advocate for the ipi? I don't have secrets Well, here's where it's here. Why I'm talking all the time about applications Right There is a great question, but I'm talking only about applications You kind of have to trust the host But bear with at least Host can be something that you want and I wanted to find but In the cases that I've been looking at simplest one or my dns or containers involved You have to trust the host there's no way the host has access to everything. It doesn't matter What happens the host will have access to all the secrets within the dns all within the containers Just another not the other way around So you have to trust the host What you have to do is that Provision of the host is not sold at home yet, but it's probably much easier to handle that Where you'll assign a credential to the whole host and then it doesn't matter how many applications around it How many he answered me you have Something you can trust there and you can build on that trust the transfer of everything So let's see an example use case that they come up Uh, they made me think of all this problem first and While in conclusion that an api is probably much better than to ensure the vision system So we had the problem of trying to get free api running containers at least just to try out if it could be made to work and Free PA by itself if you don't know what it is it's just an identity management system always, uh Like a centralized authentication system that has a ton of secrets in it And it allows you to educate all your clients and one of the features of api is that It is distributed in the sense that you can have multiple Servers that all serve the same Kind of information and they have to replicate information with each other. So When you have to set up another copy to a lot balance, you know Just for geography to distribute the service We had a pretty manual system where you go on On the existing existing server You know run a command that generates a gpg encrypted file We've all been necessary secrets to bootstrap a new server then you have to transfer this file to this new server Physically be there or Staging there putting a couple of passwords Unpack the gpg file get all these secrets out and bootstrap this new image this new server um It works it is relatively secure Uh, it's it doesn't scale in a dynamic environment. It's it's it's very hard to automate Because you have to have very few access To both the machines the one you have to install and one Existing one and it's a lot of steps. You have to do It can be kind of Plus we were adding features Like this sub-ca feature where we allow you to create multiple CA instances in the IPA where you can do that on the fly later on Once this is the whole system installed distributing, I don't know that 15 20 servers And when you create a new CA You create a new sub-ca, but that's CA when you're private key and you need to distribute that So a number of secrets we have Not only do you be distributed at the time you're creating the icon of the system But at times during normal function where you have to transfer them, you know dynamically on the fly And that doesn't work. You have to man do it So what you know the admin create a new CA and add nodes and blocks and all the servers grab this key Bring it to another server You probably do something wrong at that point So we needed to have a way to fetch Credentials from the server A second method of transfer then And a way to authorize access to these keys. These are the three main issues we have So what do I need to be able to perform these actions? Well, I need an account from the service to the services I cannot do that manually. I really need a service to do that an API that's very important I need to be able to equip this from ratio at rest pending transit I need, well, I don't technically need the rest of the API, but these days everybody does it And I need especially a modular design because what I'm thinking about this thing I can't come across other similar problems in similar application of a cyber API, but Contemporary application have these kind of problems. So I wanted something that's modular enough That it could be easy to extend with you and use it in another situation And well thinking about things like OpenShift, for example Another service that not just even infrastructure, but go all the way The user and have multi-tenancy issues. That was also the issue of being able to proxy around this data and, you know, have dynamic access control. So I wanted something very modern And so I decided to build a prototype and this prototype was the I meant to create a basic Functionality for free API, so we could use it in there, but also explore the problem space I wanted to build it as an HTTP server Mostly because the container Kubernetes Docker DevOption 1 is really involved with HTTP and it's kind of the new IP transport of the new world But I wanted it to be able to use a Linux socket Because I want to be able to use it without exposing the servers that I don't have to Next problem was how do I make sure that when I transfer secrets I can do that securely? This it was specifically important And so I started looking at what they could use to encrypt data over the wire in a way that wasn't Invented by me And I implemented JW Prickler, which is another project that just implemented also Stundam now and got standardized while I was building it And that's just a way to use JSON and a bunch of Kubernetes Do great tokens encrypt or sign or go Any data that you can have any JSON structure And have the Prickler sign based on keys you have and transmit it over the network And also key is extensive So how does it work in principle? It works as a kind of pipeline so The url you pass here is basically the address of the secret or gracious want access It could be local, but it could be hcps for example. So you have this client who wants to ask Please server one or the service one Give me the secret and It can also be It could be server immediately if you're talking to the server that actually has the secrets Or maybe that server is a mailman that simply knows How I'm aware to directly request And it just passes it on to the next server and in moon use the uri will change it and append stuff Or actually prepend stuff, never append stuff And that can go to another server And where that is useful is where you can have making part of the secrets Stored in one system and parts of another For various reasons. That's a base of which you could be asking who could be redirected to different services And you might end up translating that again into database query because both requests and Uh, we'll look at the coming and of course you can go out by five points You can transform that in what you want. And this is just an example to show how It might work So how do we transfer secrets I came up with two apis one simple in fact is all simple where you just go and contact Service and ask for a secret by name And it has it. It gives it back to you As you can see, I'm not Showing any authentication here Authentication can be from the bottom of whatever you want. It will probably be something a header. It's a plus case It's to be basic off And you send a password there Has problems But it could be off, it could be just API protected, it could be anything Or it could be just a local unit something And then you just Check what is the process on the other side? What is the sdl to make what it has on so authentication or and or authorization is kind of major and also Completely important But it's not a hard drive to do any specific authentication application And just or is he gonna say we just put And If you're allowed to do something in the namespace that you choose in this case Just Then we get back to the one okay. You put your secret or an error This is the very simple one the simple one has a single problem. Everything is in the field. So It means you can probably want to have either local connection or national connection This is not useful very much for me This is the more complex one It's still just the Get And you still have to provide the name of the secrets of authorization But Then you have to provide Something else that something else is a jwd. You can add your zone up talking Just basically assign it potentially encrypted, but in in this case i don't know about the sign requests And it's looking pretty far The protocol requires you to basically for encoding because you know You're sending you our eyes to observe us that What these three things is Jason blocks The first one is header header is not perfect It is protected that You have to be careful when you pass it because you will read it before you can verify it And it contains the public key identified Yeah, so it contains an enterprise public key that the other shows need to know And that you use your private code to sign the rest of their lists And it will also include an algorithm that you can choose There are many algorithms that are available in the hose standard You can choose one or of course on the other side you can choose to accept them Then there are the claims And this is completely arbitrary in the jwd There was a standard so this is something i came up with Hopefully it's not too stupid One is This subject has to be correspond to what you are asking So you have to put in to the request the name of the secret this way i can as a sign of name Without having to be on the green your eyes And you have to validate that otherwise so you could send a query by name another one An expression of time you want to do that because you don't want to have someone be able to capture very fast and then we fight later maybe after they were able to They could get keys two years later or something and then Now the value The value is interesting only when you're trying to put the secret When every question is secret And then you get the signature and the signature signs They're probably prepared So you really find a key Make sure the other one is valid Check the signature and then you trust And then You get to the ceiling part then The service need to send you back the secret request at this point the creature is Necessary because i don't know whether this thing is going on here or not You probably won't use dls anyway around this but it won't happen and it is another Use a web token but in this case it's using the web encryption It's more complex as five parts one is the enter signal to be used one Although in addition to the sign algorithm you also have to provide an encryption algorithm Then there is The actual encrypted key The whole blob is not encrypted directly in whatever private public private key you have but you'll create a temporary Symetry key in there Only that symmetry is encrypted with your public key in this case The service will use your public key to represent your your your your private key um initialization vector being needed by The encryption algorithm you choose so if you're wearing stdc, you'll have an id with other accounts you might not be usually doing this um cyber text That things encrypted in the key encrypted in here and an authentication fact to verify that the encryption was actually That's So that's it so That's for the problem. It's it's two basically two tokens types, and that's it now authentication I'm talking to headers usually in their creepy And here is how you Configure them there's a configuration file from stdc service, and you can say authentication header header is the name of the module It has handler, which is a python module Adventure configuration in this case. This is one of the example Um Classes which simply uses freeze the header remote user So not something you want to use Directly on network. It's more interesting where you have a proxy between you And custolia that actually does some authentication and then sticks remote user To the request There are a few of these module available in the project And then there's an example authorization directly instead. I see This is taken from the arcade project In the hasons handle it says it says that Enemy under slash keys to the uris collected by it and there is not any slash keys Just think about apply It tells you that the store can use IPA and it's another Directly that defines the store And tells you where service is basically these is used Assigning encryption tokens and where the server can point its own keys So how does it work within IPA in the end? You have one provision instead And that provision is that is storing in the IPA server Is a has that not a storage The public key that you want to trust For exchange of key material Once the admin sets the public key in LDAP The corresponding private key can make requests and accept and update any of the secrets in the IPA server And that public key has to be stored in a specific place in LDAP where only admin access is provided Then you can start Creating a new server of the replica or simply in that every is already stored. It's just a new Key it will send a request to the sign from the top of the chart before using its own public key What the study will do Is look up if that key is available in LDAP It is available in the fetch also the encryption public key because there is actually a key pair In this case Find out in the secrets of it Rub it up and craft it in the encryption. I'm going to set it back. And that's it How do we do authentication authorization in this case is interesting in the IPA case Any machine that's drawn an IPA already has a key pair So there is a basically double authentication system here One is in order to even talk to the store You must have a key tab And you must use a digital authentication against the Web server the password server where the IPA is stored If you are out of progress there Then the password server proxies your advice to the actual study network, which is recently only on the local server It certainly will check that The service sender request has the Apache uoD And has the SNS context of Apache And it will check that the remote user Patrick set actually I think it's just a slave because it's not out there so again in this case and that after it contains the actual Principal name Of the key tab that we use to authenticate That principal name allows you to go in and out and search for An entry that has that principal name in it and the two public keys So it doesn't matter Really that you send the public key in a sign or type We only allow You to access the public keys that are associated with that principal And then we double check it out correct for us. They will check the signature But if they're on the wrong keys, so if you get access to the key tab, but you don't get access To the signing keys, you still cannot access it from there The service and the bus version so you have to have both the kingdom and increase your assignment keys to get access to this stuff And that's all so You can have two containers that are pretty similar And you have something on the house, which is custodial on the house Do you trust the house? How would you differentiate? Yeah so Can explain a little better For this one So that's a good question So in this case, you can imagine that this one is a it's a local custodial server and this one is actually a container So This one will probably Be related somehow if you're using kubernetes for example docker would be related to that in the sense that When they spin a container They will tell the custodial service or maybe the custodial single query What is the container ID? So when and What is the socket this container can talk to? So when this container will contact locally on a unique socket The local custodial service, they will be now real authentication Because we ask the operating system Who is the uid on the other side? What is the socket that is coming getting on and then we can match that container at that point This one knows who's the container And then you can use for example kill as a ticket to connect with centralized custodial service and ask for give me this secret and it will augment here Either with the name of the container or more problem with the label That is associated with containers that the remote custodial service know about So if you have let's say three applications around kubernetes and you know Bunch of containers that do I don't know WordPress application budget containers that to Run a frigate here and a bunch of containers do something else Then when one of these containers can pack the remote custodial service, they will get a label that is probably a WordPress So when they will ask the next one Then we put WordPress Now this other one will know that This this server can't ask for WordPress secrets because it's one of the hosts that is allowed to ground the WordPress containers and then trust this host That he's asking before we have one of the WordPress containers that will fulfill the request If you have your setup setup your setup in the white where you have only specific host in stuff with uh more press and only specific host Do they start with free again? and the host That you know the WordPress containers pass it with free at the label the central system can say oh well That host is not allowed to ask about this information in your life So basically you have a chain of trust By which you can segment partition your infrastructure and know To reach you can be specific signal now Of course if you're running all the container on the posts Then all your trust just in the host because the host can ask for everything but that's up to you how to set up things So are you thinking of with central control and policy for that too because you have policy Right, so that's something that is not built at all and so kustan is to be flexible. So it's probably 15 months thing to build a single authorization piece And with that you can do whatever you want except for that an external system full policies or whatnot My idea is that if we can Do something like this with something like kubernetes on docker kubernetes already using dcd To do stuff and then you so you would have a policy and then we'll be already pushing the host So at least the host means we'll get that policy as well and How we get these labels in and we'll already know how to label these containers So this part is kind of simpler because all you need to do is to associate the container with some sort of label And then the only needs to know where to go next Uh, the central piece will be more complex. We don't have to have some Better understanding of who's allowed to do work but again Nothing impossible and easy to manage in the sense that they put everything in a few centralized places And you manage all the sectors there or you can say, you know, nobody can update secrets on the admin from another host all sorts of things But that's that's probably a policy system so In the kubernetes in docker kubernetes, you would have to mix that that there will be an instance of custodia serving a tenant or One well Again, that's actually the point of the decision So if you're doing your own infrastructure, you own it Up the bottom, then if you just place a custodia server on the host Everything just all to it I'm sorry, that's a good point. So even in this case if I have different applications running on top of that How I can make sure that my SQL server and my I don't know messaging server, they don't try to ask for a cigarette So as I said, you can have a lot sounds like every native of docker You will have a way to know based on the socket Who's asking for information at the very least you have the user ID of the process that's running And probably in the single label of the sbf case You have to be able to dynamically map them because every time docker runs And your container sbf has an in-landed pcs label But on the local system it's easy to discredit who's who as long as you have that information for either By someone or you have an api to request the information That's that's the only the part we have or you set up your system In a region that you always get You know specific ID you and the specific mcs labels, you know, that's up to the point Uh I think it's more interesting in this case, maybe where you have to actually over the network I decide who to but I would I would say that this case is more dynamic because of the local Random container can be run and this case is more about policy So here you apply the label and here you have a more rigid policy that has to seek a label with a tenant And so if it's all your infrastructure You're only dividing by application probably if it is a more complex system like Open sheet or not where you have actually two parts you have infrastructure people And you have a tenant and the family will have multiple applications In that case, you may have a three layer approach where you have a host system that's allowed to ask something To a container A group of containers that represent an application and each group of containers could have their own We could study a server they could with each of them that would Yeah, you're probably most probably have just one customer service per tenant Even if you have 10 of the patients you just don't want because it's you don't want to have to manage them So you will have access control ways within your customer service to know What they can help so one of the models I have called namespace It's easy Just click the local Database where you have secrets by namespace you have a I don't know what what press namespace database namespace Something else namespace These labels will trigger these namespace a lot of access your configuration file. You said you can have different authorization providers for different paths Right. Do those stack like I have a default provider slash and then Slash will be something. Yeah, they can be stacked. There are some limitations there Especially before ordering Ordering may be an issue if you want to do strange things But the nice thing is that these are patent classes So you could just give if if you cannot resolve something you can always pay the subclass and then do your own thing And I think they do that like a actually so It's kind of flexible Up to you how they want to go to your you usually probably want to I think it's in the In the idea case that you use Two authorization plugins in the same product. One checks the UID and one checks the remote On a header So I check both. That's what I have to flag it Okay, so you can set that So if both pass you're in either fails or out Okay, cool. Yeah Have you written your own? Did you have an opinion on HashiCorp's vault product? Yeah, so many people came to me when I'm writing this thing Oh, I've seen this cool vault thing and I think it's quite interesting as a project The main difference is that vault is not an API. Vault is an actual storage Solution It's true that they even they don't have one of their own database But it's not like you can proxy to a vault or anything Basically, it's the final thing. So I see custodia as something to use both in the back end So maybe you know custodia store all this stuff in vault And basically front-end vault exposing actually a simple API because For most uses you don't actually care about the ad nape and have the API in this case I mean applications just need to store it on to the sticker, but you don't have to do your access controls or anything like that So I see for example anything that mandates access controls, right? You know kind of sort of out of band Maybe not exposed And so yeah, both there is a bolt feature in IPA as well where we can store secrets Unfortunately same name and they're coming at the same time, but they both do the same thing They actually do the final step of store and something somewhere, but they don't have any of the pipeline feature Thank you So you can talk a little bit about Kubernetes, have you looked into integrating it? I haven't worked into it yet because I feel Yeah, I haven't worked in the Kubernetes yet. I've been Finishing the integration of the IPA because we actually need this For a feature that comes coming out in the next version It actually promotes the normal machine to a replica And for the sub-C8 features, I already needed to incorporate that And actually have the demonstrated API actually provides for you So now I almost done and I consider the basic IPA rather solid because it's actually tested by me It works to be the whole thing So then I concentrate on trying to expand the use to random applications and find out what's missing there So yeah, the plan is to look at Uh, probably building a modeling go so they can be Embedded by a Docker Kubernetes or what you have and Yeah Work my way in there Yeah, I don't plan to push, you know, the Docker Kubernetes or what use Python this But uh, that's what we have an IPA The core is simple so translating it to a simple type of thing Should be rather easy Will the plug-in be reusable or you would have to rewrite it? Well, no, no, the plug-in is just Python classes But the plug-ins are really, I think the most complex plug-ins probably that you guys have heard What was important for me is to create a structure that is plug-able But now when the plug-ins are in a circuit box, hopefully Hopefully it works Are there questions? Yeah, thanks