To this first episode of the HBCU Experience, I am your host, Gwendolyn Harris. I am sure some of you are wondering what this show will be about. Well, I will tell you. February is Black History Month, and there is a lot of history to be shared. I thought I would give some knowledge on something that is near and dear to me, and that is the history and knowledge of the HBCUs, otherwise known as historical black colleges and universities. HBCUs are coming to the forefront because of our Vice President Kamala Harris, who is a graduate of Howard University and HBCU. Today, we will discuss the history of these institutions of higher learning. My guest today is Dr. Catherine Waddell-Tacarov, who is a professor, author, and publisher who has great knowledge of this subject. Let's welcome Dr. Waddell-Tacarov to the show. Aloha, Dr. Tacarov, how are you? I'm just very, very good to be able to talk about black colleges with you today. I am so glad to have you here. Just tell our viewers just a little bit about yourself, just a brief summary about yourself. I was born and raised in Alabama in a college community, Tuskegee, which is also an HBCU. I had my education at a Quaker School in Pennsylvania and my undergraduate in Boston, Tufts University. And then in between, I had gone to France for a summer, Africa for a summer, and then I got married. And when I moved to Hawaii in 1968, I changed my major. I had been a French major. Changed my major to political science because I had found that lots of people here knew very little about African Americans and our successes and our contributions to society. Wow. Wow. Well, I am definitely glad to have you here today, Dr. Tacarov. I'm gonna have a hard time saying that today. I really am. You can say Dr. Catherine. Okay, Dr. Catherine. Let's do that, Dr. Catherine or Dr. T. But anyway, let's get this conversation going. As I stated before, HBCUs or historical black colleges and universities are coming to the forefront now because of our new vice president, VP Kamala Harris, who went to Howard University. And there are so many notable people that have gone to HBCUs. Martin Luther King, we've had actors, civic leaders, Martin Luther King, our actors, and just a whole lot of prominent people that have gone to HBCUs, civil rights leaders, actors, musicians, inventors, poets, and the list goes on. I'm a graduate of HBCU Hampton University and I'm a proud HBCU graduate. But Dr. Tacarov, tell us about the history of the HBCUs. Okay, I'll try and be brief. Right after the Civil War, there were black soldiers that were sent out west to carry mail and lay the groundwork for many of the public, the big parks, like Yosemite. And then other blacks who were recently freed slaves in the south saw the need for education. Remember when they came out of slavery, very few could read and write. It was against the law and people were working all the time. And so unless you had a kind white master who had kids that might teach you a little bit to read and write. Or unless there was a master who loved their offspring from a black woman and sent them away to college up north or even to Europe, there were those. People needed an education. They needed to feel a sense of community. They needed to create communities. So the consequence was that there was the beginning of the HBCUs. Let me just say that although there are historically black colleges and universities mainly established after the Civil War, there were two or three colleges that were black before the Civil War. And one of those was Lincoln University, which graduated many, many famous black people. And then another one was Cheney. So those were the two that were at the earliest stage in the north. And a point that I need to make is that HBCUs were very diverse. They thought in terms of non-white people, I guess you could say. So that at the HBCUs, there might be Native Americans. There might be some Asians, not so much in the earliest days, but certainly now Native Americans, Hispanics, just a wide variety of students, predominantly black. And what made these institutions, these young institutions, these young schools so amazing was number one, the thirst for education. People would walk from Mississippi to Alabama, from Georgia to Alabama, just to get an education. That's how strongly they felt about it. I was born and raised in Tuskegee, so I have more to say about Tuskegee. But this thirst for knowledge and for belonging and for having a sense of community and political building, I guess you could say. The HBCUs, besides those two that I mentioned, Cheney and Lincoln, were often on land grants that the government gave, not only to African American colleges, but even the University of Hawaii was early on a land grant school. So there were the public schools, and then there were a lot of religious schools that didn't preach the religion, but their supporters and their boards were often white, maybe ex-avolitionists, maybe people just who had a sense of justice and equality, and they were supportive in the building of these schools, these HBCUs. And right now, there are 107 in existence still. Right after the Civil War, there was the Reconstruction period, so you had a conflict. You had people from the Union Army, the North, that were trying to reconstruct the South, and then you had people mainly from the South who wanted to go back to how it was. And so there was violence. There was a lot of violence around that, but built, they were Lincoln in 1854, Hampton in 1868, and Tuskegee in 1881. And I wrote a poem about Tuskegee. I think I'll just read a little bit of it now and then save the rest for the end. But there was this black connection with Hampton, and you had mentioned that you would like me to talk a little bit about that. And let me say first that King Calico, no, before King Calico, King Kamehameha IV and V traveled to the mainland United States and visited Hampton University, took gifts from Hawaii, feathers, feathered capes, and various other things that are there to this day. But before that, in 1823, a slave of the president of Princeton, now Princeton University, was freed by the president, who was her master, and given free reign of his library. She educated herself pretty much, and she wanted to become a missionary. She was not accepted to go to Africa at the time, so she came to Hawaii on the second ship of missionaries in 1823. She started a school, and this is getting back to the HBCUs in a minute. She was on Maui. She started the Lahaina Luna School, which is known by everyone in the islands in Lahaina. And at that school, it was the first school for commoners, and they were called Maka Ainana. And she taught the classic math, reading, a little bit of philosophy, those kinds of subjects. But she also taught industrial arts, how to do things with your hands. And so while on Maui, she had the opportunity of meeting the Armstrongs. Perhaps she was in Honolulu. I'm sorry. I don't remember that detail. But she met two Armstrong brothers. One was William, who traveled around the world with the first monarch, King Kalakawa, to travel all the way around the world. So he was like the interpreter to the king and traveled with companion. And then the other, okay, so that one's name, common name was, what was it? The second one, this King Kameha, may have a fifth, was Lot, L-O-T. The other one, I don't remember his name, but anyway. So there were these two brothers. There was William, who was the assistant to the king and his round the world tour. And then there was a brother, who was a general in the Union army, a general. And he was the first president of Hampton University after the Civil War. He knew Betsy Stockton. He knew that her curriculum. And I think that probably going around in a circle, Betsy Stockton indirectly influenced the Armstrong brothers, who then, one of them, was the first president of Hampton. So that was just an amazing piece of research that I found out about. Yeah, go ahead and ask me a question so I don't miss anything. No, you did fine. And it's Brigadier General Samuel Armstrong, who was the first president of Hampton University. And I did, and you spoke very well. And that was April the first of 1868, when Hampton was officially founded, because originally it was called the Hampton Normal School. And before it became Hampton University, it went from Hampton Normal to Hampton Institute. And then while I was there in 84, it switched over to Hampton University. But no, you did, I'm just enjoying listening to you.  And I know there were more. There was 120, 121, I believe, at first. But because of funding, which is a big thing, for the HBCUs, a lot, a lot have closed. Maybe I can just say that students at the various colleges, and they were most of them were called Normal School in the beginning, Tuskegee was. And then it was the Institute. And finally, it's the university. They walked from another state. It was just amazing, their determination to get an education, the values that these newly freed persons, as well as there was a whole host of freed persons, already freed blacks, that were in the north in Philadelphia, or that were runaways, all the way to New York, all the way to Canada. So there was this connection with Betsy Stockton, the Armstrong's Hampton University, from Hampton, graduated many future presidents of HBCUs. And talking about one of them is Booker T. Washington, who set up the school in Alabama at Tuskegee. And my family member, I guess it would be my grandfather, who also went to Hampton, was invited by Booker T. Washington to help to establish the school. And what happened was the students built this beautiful campus and this beautiful school. And that was an exercise of the industrial arts and working as masons and as, you know, all the brick layers and all of those things. And then there were the plumbers and this, that and the other. So Tuskegee was taking off. Howard, of course, was there and was big time. I'd like to read this poem at this point, because it gives the history, as I knew it, as I lived it, kind of sort of Tuskegee. And the name of it is just Tuskegee. Tuskegee, divine mirror of two due attitudes, black folk, hard work, rewards of success, diamond of a small southern town, mind from dark slavery, sharecropping, miscegenation, and born in dreams. Tuskegee. Students walked for miles to arrive from neighboring states with one change of clothes and determination. They arrived to labor, to learn, to progress themselves and the race, to seek an education, help to build a school, a campus. Students made the bricks one by one, cultivated the grounds and built the Tuskegee Institute Chapel in 1898, renowned towering stained glass windows by a French glass designer, precious colors, royal gems. A whole community witnessed the Great Midnight Fire destruction of the Belissimo Cathedral Chapel in 1957, flames seen from my house two and a half miles away. A whole community, new fear, understood endings, listened to rumors of KKK violence, remembered, remembered burning crosses and vulnerable churches. Tuskegee, people watched the recurring tragedies of race so connected, yet disconnected by color and class, and unknown, quilted histories, whispered in closets, behind doors and bedrooms. But where was the brotherly love? Trepidations of whites dominated the unspoken discourse, fears of educated, articulate, uppity niggers who sang jubilee songs and spirituals, traveled and got degrees. Oh yes. Blacks thrived, got jobs, created jobs, researched and learned Black history, understood the value of Black pride and self-help. Chief Anderson, light-skinned and confident, taught the Tuskegee Airmen at Motenfield at Tuskegee, took up Eleanor Roosevelt in his plane. She dared to fly with a Black man. My dad, Bill Waddell, walnut brown and handsome, came to Tuskegee to work on peanut oil therapy with George Washington Carver, to research a liniment for those paralyzed by polio, like President Roosevelt, who reluctantly visited the campus with his wife, who went flying. My mom, Latte, proud, smartest of whip, fabulously stylish, from a well-to-do family who owned land and had servants, descended from generations of Black teachers. She taught languages even after marriage, French, German, English. When women were expected to stay home, she kept her job. Today, I see so many mind-to-pictures, family resemblances, processes evolving, Tuskegee, Tuskegee, my home, prototype of hard work and determination, so much history, open and hidden. Wow, thank you so much, Dr. DeFar. That is a wonderful poem. Wow, and that in itself, that poem in itself basically tells the history of Tuskegee and, of course, your family. So that is awesome. I have one question for you, though. What do you think? Because, first of all, this show, the HBCU experience, you can't do all this in one show. It's so much things that we will be talking about in this show as far, and you will see this as you continue to watch. But my question to you is, what do you think will be the future of the HBCUs? Well, I think I'd like to mention why people attend, attended, and many of those all Black universities have quite a large number of Blacks. My father was a co-founder of the Veterinary School at Tuskegee, and that was in the 1930s. But what happened now is that there are more white students at that veterinary school than there are Black students, which isn't to say there aren't Black students. There are plenty. But I'm just saying how the times have moved on, and why people would choose a Black college. And I wrote down these few little points. They get a top-notch education, STEM, engineering, medicine, nursing, psychology, political science, the arts, all of that. Second, the supportive atmosphere of the professors, of the community, and the building of a positive self-identity. Then the diversity, which I mentioned at Tuskegee, there were always some foreign students. I saw Africans. I saw people from South America, as I mentioned. I saw lots of different people, even if it was 90% Black, there was always diversity. And then affordability. Black colleges, HBCUs, although pretty expensive these days, maybe $22,000 at Tuskegee, plus room and board. But that's not like Harvard or Stanford or a state university. And the HBCUs were either public or private, as I mentioned earlier. There's a lot of alumni support. And that would help people to attend and networking. And it goes from the sororities to the fraternities to the various organizations. And people felt that they had support once leaving their undergraduate education. Then there's scholarships. And then it's location, location. If you're a part of or near a Black community, that's very nurturing and brings forth pride. And I mentioned before, but I'll mention it again, the supportive faculty. And I'd like to say, in relation to Black faculty at the University of Hawaii, there are very, very few. Almost probably 90% of the students have never had a Black professor or even a Black teacher in high school. So there are these things that still need to be worked upon to bring, if not balance, more equity in the educational system in Hawaii, that we have. What you say is true. And this is one of the segments that we'll have on one of the shows as why people attend an HBCU. Because like you say, it's not all Black people. Even when I went back in the 80s, we had people of other races to attend Hampton University. I say Hampton University, Hampton University. So it is very diverse. And I can tell you really quickly why I went to a HBCU is because growing up, I went to predominantly white schools. And I just, I got accepted to all these different other colleges, big time colleges. But when it came down, when my mother and I went to go visit Hampton, as soon as I stepped foot on that campus, I was like, this is where I wanted to go. And as soon as I got that acceptance letter, I think a few weeks later, that was out of all the other college acceptance I received, that was my favorable one. And that I can tell you is lifelong friendships at an HBCU.  But like I say, it's a lifetime friendships, you know, and that's 30 plus years, you know, I'm still friends, friends with my people there. Another attraction I think of the HBCUs is the campus itself, not just the campus life, not just the great professors that care about you, and don't dismiss your attitudes and ideas. But you learn this, this black history that is so rich. Now it's much more available since, you know, Carter G. Woodson and all of that. I mean, it's really become much more available. But research continues. And the research is phenomenal. My research was on blacks in Hawaii. And that took me a long ways with publishing articles and doing a lot of oral histories, because our tradition is an oral history tradition. I say, I say of myself that I'm an Afrofuturist, Afrofuturist. And I say that because the traditions of black people, and many people in fact, is an oral tradition. And through my poetry and public speaking, I feel that I use that tradition from the past, bring it to my my present, through my teaching and through my public presence, and then to think that that in turn influences the future. I mean, we can look back at jazz musicians. They were futurists. They felt and divined chords and rhythms and things that were not available somewhere else. And so this tradition of song, of dance, of storytelling, of history telling is so very rich. And it's across the African diaspora. It is. It's just so there. So Dr. T, if people want to find out more about HBCUs, where can they go for that information? Well, the easiest thing, of course, is to Google HBCUs. There's many, many, probably hundreds of pages there as they break down the different colleges and what they have to offer and blah, blah. But also, I think that people need to get more out from themselves and their particular community. I think that if Black people and local people of the diverse ethnicities and races, if they talked more together, then that would be an education on both sides. My history in ethnic studies was that I started out teaching Black studies and introducing courses of Black studies. But I had to learn, and joyfully, it was a great blessing, the history of the Native Americans, the Native Hawaiians, the Mexican Americans, the Chinese and Japanese Americans, the South Pacific Islanders. It's so important to begin to see connections, not just differences. The diversity enhances the expansion of the mind, the consciousness, and the vision that, hey, I can go beyond. Well, Dr. Takara, I thank you so much for being here on this first episode of the HBCU experience. Thank you, thank you, thank you. I've learned a lot just by talking with you, and I hope to have you back for some other shows. Thank you. Thank you so much. And don't forget to ask your viewers to send a note or text or something as to whether they found it instructive and what areas they might be interested in. So you heard that from my viewers from my first show. If you like the show, if you have any other questions that you want to know about HBCUs, which I'm sure we're going to cover in future episodes, just drop a line and let us know. But until next time, I thank you all for tuning in to this first episode, and I hope to see you again next time. Until then, aloha and God bless.


Hi, I'm Zor. Welcome to UNISOR education. This lecture is part of the advanced mathematics course for high school students. I recommend you to go to UNISOR.com to watch this lecture, because it's just part of the whole course and obviously all lectures are interdependent. So take the course. Well, in this particular case, I would like to continue talking about statistical evaluation of Bernoulli experiments. In particular, I would like to use something which we have studied before called sample variance to evaluate, much better evaluate the variance of the sample in order to more precisely evaluate the margin of error. It's very important actually, because more precise evaluation of the margin of error or with a given margin of error evaluate more precisely how many experiments you need to achieve this particular margin of error. So that's all very important and the difference between my old approach where I was just evaluating very crudely the number of experiments or margin of error just based on number of experiments without regard of what kind of experiments I have, without regard to the data. So I expect that evaluation would be much more precise and better and that's actually how people do it in real life more often than crudely the variation we were talking about before. And I will talk about exactly the same three problems which were presented before a couple of lectures ago and I was solving these problems based on, as I was saying, a crude methodology. Crude methodology actually was, let me just remind you that if you have let's say a random variable like C which takes value 1 and 0 with probabilities p and 1 minus p then to evaluate p for instance with certain margin of error we have conducted n experiments and the results of these experiments are also 1s and 0s, right? So their sum divided by the number n is actually a frequency of occurring this particular event, right? Because it occurs and the x is equal to 1 and it doesn't occur x is equal to 0 so sum of 1s is actually number of occurrences divided by n is frequency and frequency is something which we were using to define the probability, right? This probability p, it's kind of a limit of the frequency as number of experiments goes to infinity. So we have conducted n experiments and now we are saying that, well, yes, we understand that if n goes to infinity that frequency would probably go to p but since we are not in an infinite situation we are in a finite situation the question is how close this is to this Well, to evaluate this we have considered an independent identically distributed variable c1, cn identically distributed of these ones and consider this particular random variable, eta so basically this is a single value of this random variable, right? Now, if this random variable which we can basically evaluate in some way if this random variable has a very small variance then the frequency with a high probability lives within the vicinity of the mean of this Now, mean obviously is the same as p because mean that everyone is p so it's n times p divided by n so it's p and that's why we can say that this particular value of this particular variable, random variable might be close to its mean value if variance is small Now, variance of this we were calculating before it's p times 1 minus p divided by n so variance goes to 0 as n goes to infinity so it's quite reasonable to assume that with large n variance would be small and variance is basically a measurement of how far from the mean our random variables actually lie so we were approximating with a normal variable this thing, because it's sum of independent identically distributed variables so it's distribution very close to normal so we can consider a normal variable with the same mean and the same variance and then I made a very crude evaluation of this variance since p times 1 minus p is always less than or equal to 1 quarter when p is from 0 to 1 then the whole thing is evaluated this way so now I know basically the variance of our almost normal variable and know its mean and since the variance in this particular case is evaluated from above using only n then I can use something like a 2 sigma rule 2 sigma rule and say that with probability 0.0 what was it? 9 to 5, 45 my probability of my eta to be within vicinity of this mean, this probability to be vicinity less than 2 sigma so this probability is higher than 0.95, 45 so that's a variation of margin of error and the certainty level we can say that our random variable lies within this margin of error from its mean which is p so I can say that whenever I have calculated this based on my experiments with probability 0.95, 45 it's very close to the p which I would like to evaluate with margin of error equals to 2 sigma now if variance is this then 2 sigma would be 1 over 2 square root of n so it's square root of this standard deviation so that's my variation based on this relatively rude margin top margin for my variance now this is good if p is very close to 1 half if it's equal to 1 half, it's equal to 1 fourth, right? but if p is small this becomes a very, very crude evaluation and it results in the necessity to have a very large number of experiments to achieve the same margin of error which we desire so let me now switch from this to more precise evaluation of my variance using this sample and you will see what kind of results we will get we will get much better results with small p's and these are my three little problems which I have presented before using the crude evaluation of the variance and now we will do it with more precise evaluation based on the sample which we have received so now if we have received a sample x1, etc. xn what we do first to approximate the variance first we do approximation of mean that's what you know and then we do the approximation as square equals to x1 minus m square plus, etc. plus xn minus m square divided by m so this is my approximation of the variance right? now we have already discussed that if this is Sn Sn is actually the evaluation of the variance which is not exactly having the mean value the same as the unknown variance so it's kind of skewed a little bit right? biased as we say and Sn minus 1 which is the same numerator but the denominator is n minus 1 this is unbiased evaluation so we will use this evaluation of the variance now let's use this particular variation in our three problems so the problem number one is I don't really need this I will use this real estate for the problems so the problem number one is we have 10,000 experiments we are manufacturing parts and the experiment is whether the part is defective or not and let's say we've got 300 defective parts now I would like to evaluate with certainty level 0.9545 what is the probability of my part to be defective based on this particular sampling well first what we do is calculate the arithmetic average of this and this is 300 divided by 10,000 which is 0.03 so this is basically our evaluation of the probability of manufacturing defective part 300s question is how good it is what's the margin of error of this particular evaluation now what is m well as I was saying before m is equal to x1 plus etc plus xn divided by n this is a single value of this variable where all c's are identically distributed and independent variables exactly as our unknown one so now I would like to evaluate the quality of approximation my probability with this number m based on the variance of eta so let's calculate so the sample variance and I will put n minus 1 here in this case now what is this well we have experiments 300 times when our variable took the value of 1 so its difference square from the mean is this one and other 9000 sorry 700 we have a value of 0 and we have to divide it by 9999 because this is n minus 1 so it's 9999 so this is our evaluation of variance of our variable c original one now how about variance of eta now we know it's the variance of c divided by n where n is number of experiments because eta is c1 plus c2 etc plus cn divided by n and the variance of sum is equal to 1 over n square in this particular case and then n variances of c so it would be 1 over n so now what I'm actually interested in is not really variance of eta but standard deviation of eta so which is square root of variance of c divided by n so we have to make the calculation of this one and I think I did it it's 0.0291 so this is 0.97 times 300 which is almost like 280, 290 something like this and this is very close to 0 so it's approximately that's what it is 291, 10000 so what I have to do now is I have to divide it by 10000 and extract the square root so that would be 0.0291 divided by 10000 and have a square root and that my calculations show is 0.0017 so this is sigma now I need this certainty level which is corresponding to 2 sigma in normal distribution so 2 sigma of eta would be 0.0034 so what I can say right now is that with probability with certainty level I would rather say 0.9545 I can say that unknown probability of my part to be defective is within 0.0334 and 0.0266 now let me remind you that the margin of error when I was using a crude evaluation of my variance in the first way how I solved this problem without using the sample variance just using this so n is 10000 so it's 1 over 200 so double sigma is 100 so in that old evaluation I had 0.0204 which is a wider margin of error so as you see my empirical evaluation is really with this level of certainty is really much better if I'm using the more precise evaluation of the variance so if I do it more precisely using the sample variance I can say more precisely where is my real probability is so more precisely evaluating of the margin of the variance leads to more precise evaluation of the p this is a wider interval this is a more narrow interval and that's definitely is desired so with the same certainty level using more precise calculations gives more precise evaluation of unknown probability p alright? now the second problem is basically the same as this one all I have to do is what if I would like to have my evaluation even twice smaller than the previous one the previous one was 0.034 I would like to have it so I would like this evaluation 2, 8, 3 so I'm adding 17.000 plus and 17.000 minus to the mean value so I'm making my interval a narrower twice as narrow as before question is what's the certainty level I have to attribute to this evaluation well so now this was before it was 2 sigma 0.034 right? that gave me this particular certainty level here what I'm looking for I'm looking for 34 so I'm looking for this margin of error so I'm narrowing interval from 2 sigma around mean to 1 sigma around mean and as you remember the certainty level of this is obviously smaller if I'm making a more narrow interval my certainty level obviously should be less so this is the certainty level for this particular margin of error so in this particular case I get number of experiments level of certainty and I have determined the margin of error the second problem was I don't have level of certainty I define my margin of error and then I derive the certainty level as being this one it's smaller obviously now the third problem was to vary the number of experiments if I have defined for myself level of certainty and margin of error so let's do this so as before and experiments produce certain results now I would like with this with this level of certainty define how many experiments I should get to get margin of error equal 1000s so before if you remember my margin of error was 0.0034 which is more than times greater than this so I would like to have a very narrow interval but I would still like to have this level of certainty which necessitates increase of the number of experiments now let's do the very rude calculations of how many experiments I need without using the sample variance I think the lecture the material which I was doing in the previous lecture when I introduced these two problems first so if I would like this and I would like this certainty level then my sigma is supposed to be half of this so delta should be 2 sigma which means 0.005 that's something which I would like to have which is supposed to be this right so what's the n well it's 1000 so it's 1000 so n is equal to 1 million alright so I need a million experiments to achieve this particular margin of error with this certainty level well it's a lot nobody is doing million experiments I bet now why is such a big number well primarily because we were using a very crude evaluation of our variance now what I'm asking is let's do the sample variance which is more precise evaluation right and try to basically reduce this number of experiments now what's the problem well the problem is we don't have experiments we have not started our experimentation we don't have data x1 et cetera xn to calculate the sample variance so it looks like I cannot calculate the sample variance and this is the only way I have to do well that's not exactly true because what we can do is we can start experimenting stop at certain level reasonable ok and then we will have some data and try to evaluate the sample variance based on these data which we will obtain and then if it's necessary we will continue experimentation to the number which is desired to get more precise evaluation so in this case I'm suggesting to the following let's just have 100 experiments alright see what our data is then based on this data we will calculate sample variance and then that would be something to start our calculations right ok so let's consider we have 100 experiments and we have 4 defective parts ok now then I define based on these my sample variance well very simply the sample variance of Xe approximately is S square 99 right I divide by 99 which is equal to what 4 times I get 1 minus 0.04 by the way 4 divided by 100 is 0.04 so that's my M square plus 96 times I've got 0 and we have to divide it by 99 so that's my sample variance of the variable random variable Xe which I have calculated somewhere ok 0.0388 ok now now what should I do now I need sigma of eta which is sum of Xe1, Xe2 etc divided by 100 so I have 2 divided by 100 and take the square root of it which is 0.0197 ok fine so this is my sample variance of my 100 experiments now which sample variance do I need well I need sample variance 1 half of delta which is 0.0005 right with this level of certainty my margin of error should be 2 sigma well obviously this is significantly higher than this one so obviously with 100 experiments we have not achieved the precision we need margin of error would be like 0.4 or something like this alright so what do we do well let's think about this way this is about 3 times larger than this this is 5, 10,000 this is almost 200 2,000 so ratio is 40 I have to reduce my standard deviation by the factor of 40 now we know that the standard deviation of eta is 1 over n standard deviation which is square root of this so it's 1 over square root of this standard deviation of xi right so this is very important which actually means that my standard deviation of empirical average which is eta is proportional to 1 over square root of n so if I would like to reduce by 40 times I have to really have 40 square more experiments so I have to conduct 1,600 times more experiments than I have already achieved because my standard deviation is proportional to reverse proportional to square root of number of experiments so if I have conducted 100 experiments and got this standard deviation to achieve this which is 40 times less I need 1,600 more times to conduct the same experiment which is 100 so it's 100 times 1600 so it will be 100 times 1600 which is 160,000 now look at this 160,000 if you remember the crude evaluation of my variance based on just number of experiments gave a million so 160,000 is much less than a million it's still a lot but first of all let's just think about it 160,000 experiments even with a very good precision we will have evaluation within 1000s so from 0.04 before we were talking about 0.03 anyway this is something which we are considering as a real approximate value so whatever we have done 160,000 times we will add them up together divide by 160,000 and we will get some evaluation this or this or something like this and what we are talking about that around this particular value the margin of error is 100 so for instance if we've got 4,800 out of 116,000 it's a round number because this is equal to 0.03 right? yeah, 300 so now I can say that it's with this particular level of certainty my probability lies around 0.03 and the margin of error is this one which is from 0.029 to 0.031 which is really relatively precise evaluation if we are talking that the probability of something is around 0.3 plus or minus 1000s it's a very good evaluation but to achieve this evaluation you need so many experiments you see now what do you think the precision would be acceptable for you? if you are talking about defective numbers for instance and if you have 0.03 like 3 out of 100 approximately now which precision would be considered to be really important for you informative if I will say that the probability of getting the defective part is 0.03 based on my experiments plus or minus 0.01 which is from 0.2 to 0.4 is it a good evaluation? I don't think so so 10,000 experiments before gave me this with a crude evaluation now even with a precision evaluation it's still using the sample variance it was 0.0034 so it's from 0.0266 to 0.0334 it's still very large distance between these if I will evaluate two different manufacturing facilities and one would be this and another would be with the same precision let's say this 0.03 so it's 3466 44 I'm not sure now, you see which one is better well I have no idea which one is better because these intervals overlap and this one is so these are overlapping now since they are overlapping I cannot distinguish one from another with a level of certain 0.9545 but if my evaluation is narrower and the situation is this, that's one and another one would be something like this now these intervals are not overlapping because this maximum is 0.031 and the minimum of this is 0.031 so intervals are like this 0.029 0.031 and 0.033 so this is my one manufacturing facility, this one and this is one another manufacturing facility so this one all these probabilities are smaller than all these probabilities well except this one but it's just considered to be just one point and definitely say that this is worse than this because in this case my probability of making a defective part is always less so that's why it's very important to have this precision and precision requires experimentation and as you saw in this relatively practical case, well 3 out of 100 that's normal I would say for a defective part, right? it requires 160 thousand experiments to have a reasonable level of precision now let me just go back to some practical situations, we have all these statistical variations in pharmaceutical industry and in some other cases and we are not dealing with 160 thousand experiments we are dealing with much less which means that the level of certainty is significantly less than 5 or something and if that's true well we have to actually make our conclusions based on these certainty levels and the margin of errors and it's not easy that's why all these statistical evaluation of let's say new drugs on the market or something like this they are not precise they are working in some cases in other cases we do not have sufficient amount of data to be certain about certain concrete results of let's say drugs or something like this so I would suggest you to read again the calculations which I am presenting in the notes for this lecture on unison.com and other than that would probably be the end of the Bernoulli statistical distributions analysis and we will go into some other things thanks very much and good luck


Well, hey, how's it going? How's the offense? I guess getting the wrestling game back from tracks to be what does the coach call it? Easy narrative, yeah. Sir, yeah. There you go.  Unfortunately, last week, we had our opportunities in the red area, and when you come away the way that we did, you don't get the result that you want. And so obviously, each week, regardless of what happened the previous week, you want to go out and you want to execute at a high level and you want to score points. Regardless, if you had a great game the week before and scored a lot of points or you didn't. So going in, the focus has been on attention to our details and the fundamentals and making sure that we're on top of it. And when execution needs to be at a high level, specifically in those situational football areas, making sure that we stay on top of it. And the same thing goes for the coaches, making sure that we're putting our players in the best position in terms of design and things of that nature. So we're always evaluating not just the players but ourselves and move forward each week and again, try to find a way against the good team to score a good defense, to score points. I know you can't, it was not a matchup deal. I mean, were they, was that a... No, I think it came down to the fact that, again, give them credit. They did take some things away, obviously. That's a good football team last week, San Francisco. We also had our opportunities. And we just, we were a tick off here or there for making the play. And again, you score touchdowns down there. The outcome, the outlook, things feel different as the game progresses. And again, it's our objective each week to make sure that we get points down there. Just generally, kind of big picture, was it been like to work with a venture like Matt 14 games, Oxy's and stuff, work, got it, you know? Yeah, he's been awesome. I mean, I think I've said that from day one. I think with the, you always, when you're on different teams and you're coaching that position, you obviously study guys throughout the league. And Matt has been one just because of the similar offenses that Matt had run that we at that time were running in different places that we're at. I would use Matt in the cut-ups. I would show his footwork. I would show his eyes. I would show his ball handling. To be able now to work with him and to see how much pride he takes in every detail that goes in to just preparing himself for practice, let alone a game. You have a much appreciation for someone like that from afar, but when you get a chance to actually sit there and watch him and observe and coach him, he's everything as you can imagine in terms of their professional. He goes about it the right way. He never cheats the game. What I mean by that is if it's a practice rep, if it's a game rep, he has given you everything he's got in every play. And if that's carrying out a fake, if that's getting in the right check, whatever it is mentally or physically, he never cheats a snap. And that's probably the biggest compliment that I could give anyone, let alone, obviously, a quarterback and math stature. Arthur yesterday, he made the comment that he kind of thinks that Kyle is just scratching the surface of the player that he can be. And do you feel the same? And kind of what's the evidence of that? Maybe something that we don't even see. Sure, I think, you know, obviously it's, I go back to this, right?   And so having to deal with all that as a rookie, that's a lot, especially when you're 20 at the time we drafted Kyle. And then now you go into an NFL, OTAs, training camps, which he's never gone through, right? So every day, right, is a new experience. So what you hope is for all second year players, specifically ones that are as young as some of the ones that we have, that in the second year, they now know what an off season, okay, I don't have these obligations of getting ready for a draft or doing these workouts. Like now, right, I've got my schedule, I know when I have to be in the building again, I know what my OTA schedule can look like, I know what training camps can look like. So I think it's just the ability to come back with an understanding of what's next. When you're going through it the first time, I mean, head on a swivel, right? So the reality is you hope that part of the process, as I look at Kyle, right, that part is settled because he'll now know as he's going through his second year, what to expect, understanding of seasons along season, how to take care of your body, understanding that what training camp is now, what we're asking for you to do. And so when you put all that together, and then now you go ahead and say he's a year older, a year stronger, a year wiser, from a physical and mental standpoint of the game, I think now all of a sudden you can see some things maybe happen faster or easier, or hey, I've got experience. I know when I did that last time, last year, this is what happened to me. I'm not gonna do that this year. And so he'll have a whole season to go back and watch the film and study himself and how he improved and what he needs to improve on and things that he's done well and continue to do well. So to me, that's where you see typically, I was told this a long time ago when I was a player, most jumps for NFL players happen from year one to year two for a quarterback, some are different from year two to year three. So the reality is you got a lot of things off the field that potentially could be different and settled and different mindset and then obviously on the field, you get a whole year of cut-ups to watch yourself. So I think from a long way to answer your question, I just think there's a lot of things that now he can anticipate, which before he does going in for the first time, you just don't know. Right, and I think kind of going off of the, you know, there's always that expectation for the number four overall draft fit that's put on a guy whether you want it or not. And Arger was saying, you know, a lot of guys can't handle that, but Kyle can. How do you see him kind of handling that within himself? Yeah, I guess the best way I can explain it for obviously being in the building with him all the time is Kyle is more than likely the same person every day. So you get a consistency there and you appreciate people who are consistent. Doesn't mean you're not having a bad day once in a while or having like a really good day and there's something in between. The reality is like, when you see Kyle, you know what to expect in the building. You know how he's gonna be in a meeting. He'll be at 10 of you asking questions and then when he's out in the field, you're now understanding how he's going about a practice. So to me, the consistency level is important as a rookie just because you're getting pulled in a lot of different directions, especially when you're a highest pick as that. But I would say anybody in the NFL, once you get here, the reality is, yeah, no doubt, people wanna know how you got there. But then after that, they wanna see if you can produce, right? So I think there's a story that's written about when you get here, but the reality is, most people only care about once you get here, what do you do with it? And I think Kyle is just going about putting his head down, trying to be fundamentally sound, do what the coaches ask and make the plays that are given and he'll can obviously continue to trend that way. You sent him or any of the young guys home with a checklist, whenever the season ends, an off-season checklist to say this, you might look at these things or do you just say we'll see you when you get back? Yeah, no, I mean, obviously, we have to go through it first as coaches. So we typically do no different because right when the season ends, right? You obviously have, there's an evaluation process of your own roster. There's obviously an evaluation process of the free agents that are coming out that are not on your team. And then obviously you're into the college route. So it's a true evaluation period. You evaluate not just the players, but your scheme and your design and everything else that goes in it. Then you obviously you're watching each player, the guys that you know are under contract, that'll be back, there's definitely a report that you'll talk about and you'll share with that player the good, the things that he can improve on. And obviously when they're back in the building, you share it with them and it gives them a chance to work on some of those things and you build tapes for them and you help them with their craft. At the end of the day, I think most players will tell you, regardless of the background of the coach, if he thinks that person can help him or that he or she can help him as a coach, it doesn't matter. So I think that's what we're trying to provide is the ability to help that player when they come back in the building. Seize it into using Cordero's Swiss Army knife with a little bit of perspective now. What's impressing most about how he's made this transition? Usually that's a Rothstein question. And we're now here. So good. I love it. We brought in another guy for the CP question. No, it's again. It's that area. It's that area. I love it. No, I thought it was planned. Nice job, D. D-led planned that right there. Look, the one thing I have said about C is that he's a football player first. So when you're a football player first, I mean, as you're not really defined by necessarily a position, you've got a feel. And when he's out there with the things that we asked him to do, what I think is pretty interesting is you got a guy who's now committed 100% to being in the running back room. But then all of a sudden, right, he might be put out in the formation and he has to rely back on his experience as a wide receiver, which he was drafting this league to play. And what you admire about him, what I appreciate about him is his willingness, his want, and how he plays the game.  And again, I've known him for a long time. I appreciate the person. But I think his teammates appreciate the same thing that I think the coach has always seen his value and how the guy interacts, how he is as a teammate. And again, I'm glad that he's having the production and when he's gotten opportunity. He's just a guy that through the years, not just myself, but other guys have always seen as a potential man. This is a difference maker. And at times this year, he's obviously have been for us. Yeah, I mean, I think what's unique about some of these guys who can flex is there's a mental part that I think you have to be able to handle. It's one thing to see it on a piece of paper and say, yeah, I can do it. The reality is the game happens fast. So if you're all of a sudden put in a position that you don't have a ton of experience in, I just think that takes a very certain type of person that can handle that. Didn't grow up playing it. So there's not a lot of equity built into how you play the position. I think at the end of the day, what you see is you're looking for certain traits, right? You're looking for a guy who can be dynamic with a ball in his hands, but he can be physical. He can be a difference maker. He makes defenses change how they play. There's a lot of great college players that come in the NFL. The reality is when they finally get into position to be that most guys can't handle doing more than one thing. And I think as CP has gotten older, I think he's gotten the appreciation, the experience and the understanding of how to do that. I just think it's a tough task to bring in somebody, especially right from college to be able to do that. Maybe you can groom someone and help someone that way. It's just, it'll be interesting how the league moves forward with it for sure. No. It's possible. I'm gonna run it back. It seems that he, more than anybody I can remember, is down by forward progress and doesn't actually get tackled a ton. He doesn't get tackled to the ground more than most guys I've seen. Am I making that up or is there a reason for that? Is that balance? Is that balance he runs upright? Is that? Yeah, I don't. I haven't looked or thought of it that way. What I see is he's 230 pounds, maybe 235 he ate the night before some of the things that he goes. But the reality is physical player, right? So once contacts made, here's the one thing I do know.  And CP doesn't shy away from contact. And that's what goes back to the fact of just being a football player. He knows how to play, but the reality is he's not, he tries to play the right way. That's obviously not what y'all want. And the, when you look at the numbers, I think it was like one for seven with like a yard to go that left this past week. And what do you kind of just say to this unit when you're in those situations where the margin of error is that small to kind of just get the job done in this situation? I will go back and you guys will remember 2021 of me saying the same thing about fundamentals. I just, execution obviously is important. You practice the looks that you get and sometimes defenses prepare a different look than maybe you haven't seen on film. And then you use your rules as a player to adjust to whatever you just saw. But it will always come down regardless of position at all 11 is it starts with your stance from the time you were whatever age you started playing football to how you take your first step to where your eyes go. And that's just a pure fundamentals of it all. So the reality is regardless of it's 31, second in one, first in one, regardless of that situation or just the entirety of the game, the team that plays with good fundamentals discipline detailed, not saying the ball doesn't bounce a different way sometimes but the reality is you're more successful than you're not. When you get out of your fundamentals where your eyes are in the wrong spot where you don't take a great first step, more than likely there's gonna be inconsistency. And so that's what we continue to strive for regardless of the situation is the consistency of the fundamentals of not just the body but the eyes and knowing what you need to do and applying your rules. So moving forward, that's been our what we've been telling guys and it'll continue to be what we tell guys.


Hi there, it's Sandy Alnok with a Sunday card instead of a Monday card for a day early because I wanted to be here to remind you to go over to Ellen Hudson's channel to see my other video. And this is the card I'm making today. I sneak peeked on Friday. So I'm going to be using these beautiful hexagonal shaped stamps. Oh, I'm so excited that there's a hexagon shaped item that fits in a hexagon die now that we have hexagon frame dies.  And I'm going to stamp them in my MISTI so I can get them as close as possible to correct. And I am terrible at lining up any kind of die and any kind of stamp. So they're not going to be perfect, but that actually led to a really interesting solution. So I'm stamping them in a bunch of different distress inks. And then just inking the edges. Look at that. I'm filling in any of those edges so nobody's going to know that my stamping was not perfectly centered. That also is going to give it a little difference from the frames because I'm going to have the frames around them in the card. So this is going to give them a little more of a heavy outline around the outside edges just to have that little bit of inking done. Very cool, huh? I wanted something loose on the card though because all of this was very regimented in the hexagons and I wanted something contrasting to that. So I decided to try ink smushing. A lot of people do ink smushing all the time and I don't think I've ever ink smushed. Maybe I have. I don't know. I can't remember if I have. So I got out my craft assistant and I threw on the same inks that I used for stamping all of the hexagons and just threw little bits and pieces of ink, little blobs on there and then wet it with a little bit of spray of water and then smushed a piece of watercolor paper on it and moved it around a little bit. So I could get a background that just had some smushiness on it and it came out really pretty, like rainbow-ish. I thought, let me see if I can blow out one end. So I had one end that has hard edges and one end that has soft so I could decide when I put the card together which way was going to make more sense, which side I wanted sticking out because I had a vision in my mind for having like half the card with the hexagons and then the other half with something loose and splashy. So for the rest of this, while the background is drying, I thought I'd take my brush and a little bit of water and just go over some of the leaves and flowers in these. It's going to make them feel like they've been water-colored even though all I'm doing is putting water right over top of the Distress Ink and this is a really easy technique. It's super, super simple. Lots of people probably already know how to do it but it looks really beautiful on these designs. Aren't they just gorgeous? If you're a quilter, I think you might need these. I'm just going to say that because even if, well, if you're not a quilter, this might be your only quilting. This is going to be my only quilting because I don't sew. So now I've chosen a piece of cardstock to use for my background that I'm going to glue all this down to. And before I peeled off that backing, I wanted to arrange my hexagons and see where alignment needed to be because I wanted to see if I could get this to be kind of even. And it looks like I get a little hangover on the bottom and the top from each one. So at least I know where to start so that I have an even spread of all of my hexagons. So I'm going to start by putting one on here, you know, knowing that I'm going to cut off the outside edges on the left and right. So I'm not really worried about that. I just want a strip of hexagons, you know, kind of two beside each other and making that top one hangover just a little tiny bit the way I did when I laid everything out and then glue these down really carefully so that they're touching each other. And this sticky back stuff is like super sticky. It's the same stuff as in score tape, but it comes in sheets. And it's kind of crazy sticky. So once you put it down, you ain't getting it back up for the most part, especially if you press it down. So I'm going to get my strips all completely in here. And then all I have to do is tuck in all of my designs. Well, how do I know which color I'm going to put next to which color? I laid them all out beforehand in strips so I can kind of see what color rotation. So I didn't have, you know, two of one color right next to each other, that kind of thing.  Nothing's popping out. And I have a beautiful arrangement for my card. Now this alone could be beautiful, except now I have all this sticky back on the left and right. There's other ways that you can probably figure out to do this kind of a thing. But I was already planning to do some cutting out. This is really straight, easy cutting, just little straight lines. So I figured it wasn't too bad for fussy cutting at all. So did that. You could also just do this by taping everything together on the backs and, you know, just using lots of scotch tape. But this seemed like it would be a little quicker. So there I have my strip. And I kept turning my background paper different directions to see which way I liked it better. And I liked that hard edge showing out on the right a little bit. And so I've then trimmed the whole thing down, so I have nice square top and bottom and left the border of the card base showing on the left and right. And then my sentiment is half glued down with just regular adhesive. And then on the right hand side, there's a little bit of dimensional adhesive. And then I just trimmed off that little piece that was hanging out. That was all there was to it. I chose a sentiment specifically for a friend of mine. She's getting ready to start a new business. And it involves sewing. And I thought this would be absolutely perfect for her. I was tickled when I saw this stamp set in the new Ellen Hudson release. If you'd like to go see me color some tulips over on Ellen's channel, you can do that. There's a link in the doobly-doo to that as well as all of the supplies that I used to make today's card. Make sure you hit the like button and subscribe if you have not yet done so. And I will see you again really soon. Take care.