This is a great way to teach math. Too many professors rely on POWER POINTS with explanations and definitions and one example. That is an easy way out that offers very little learning. Math teachers need to be engaging and not drones! Great job Professor Leonard!
I am addict to your teaching now. I feel happy to think about to watch and learn. What a great teacher you are. I am so lucky to find these videos. May God always bless you with health, wealth and prosperity Ameen.
WOW! I'm speechless, what the heck did we study then this whole time? nothing.. That moment when your teachers suck.. I should've just watched these videos and never went to class.. Thanks for posting them!~
dear professor leonard, i'm not sure if you're going to see this but i just want to say thank you from the bottom of my heart. a few years ago during the summer after freshman year of college, i was taking a calculus 3 class. i stumbled upon your videos and found them to be immensely helpful. once i finished the class, i thought i would never need your help again. well, here i am now. i'm a senior in college with just 1 more semester to go. i put off a statistics class because i was never good at probability & stats and i was afraid of it. once again, your videos have/are helping me. thank you so much. who knows when i will see you again.
These lectures are extremely helpful. My prof teaches directly from r studio which is hard for me to understand. I truly appreciate this style of teaching.
My math teacher acted almost as if he was talking to himself or something. He just stood there with a blank face and talked with a low monotonous voice - he didn't even show signs of annoyance or anything tangible like that, he was just on complete autopilot the whole time, like a robot.
Just found your videos and they are helping me SO much!! I appreciate how thorough you are and how you break things down into simple English terms. Thankyou!!
Thank you for still helping students worldwide, i found you through reddit suggestions from people across the globe. Who, like me, do NOT have the best professor..
Ok, I've been watching the videos from the start and someone (who I guess is the same person) keeps yawning in every single video. Please grab some coffee and focus on this awesome teacher!!
what an incredible teacher! Thank you for sharing and braking things down. My professors teach like we already know it. I swear my whole class is failing.
Allow me to clarify the difference between discrete and continuous variables (or whatever else) a bit more clear and rigorously.: A discrete variable can take only certain values AND no values IN BETWEEN. Like the set of Natural numbers or Integer numbers. Given two contiguous values, there is no value in between. Also, just like naturals and integers, their possible values could go up to infinity, no problem. And still be discrete. A continuous variable can take infinite values as well, both positive and negative. However, given any two values, there are INFINITE values in between. And they are all valid. The set of real numbers is an example. One could say the set of fractions or rational numbers can have infinite values in between. Yes. But the set of real numbers also include values that cannot be represented by a fraction, such as "pi" or "e", but that's a bit beside the point. However, it is relevant in the sense that the only set that is really continuous is the set of real numbers, including the aforementioned irrationals. From this discussion it can be seen that the continuous vs. discrete random variables are actually based in number theory, in the sense that the same features seen in Integers and in Reals are the same characteristics between discrete and continuous random variables. Discrete values are a (sub)set of Integers, and continuous values belong to the (sub)set of Reals. What is so difficult about explaining discrete vs continuous random variables in these terms? After all, statistics is solidly based in math. Let's use the tools that math already provide!
I wanted to scream and tell your class that there has to be a whole 100%! 😆 (at around the 21min mark and I'm a ding dong in this. What I mean by that is you're doing the GREATEST job teaching me! Thank you!!!)
I strongly disagree with you on 40:16. Expected value in general doesn't show which numbers are more frequent, the easiest way to see it is to compute an expectation for the fair die. All sides have probability 1/6, expectation is 3.5. Does that mean that most frequent sides are 3 and 4? Well, of course not, all sides are equally probable, you cannot pick any special side to be more frequent. I think of expectation in the following way: 'if you have the game where you accumulate points (our random variable) across multiple throws ( or experiments, if we're talking in general), the number of points that you'll get on average with k throws is equal to k multiplied by expectation'. So, saying that it shows most probable value is incorrect, it's the value you would kinda get in a long run. Here's another example, let's assume that we have a three sided die with values 0, 100 and 10000 on the sides. The die is unfair, if falls on zero 98% of the time, 1% of the time on 100 and 1% of the time on 10000. If we compute mean for that die we will get 0*0.98+100*0.01+10000*0.01 = 101. Does that mean that 100 will be the most frequent value (as it is closest to the mean)? Well, certainly not 98% of the time it is. Also one more thing to note, I think your chances of getting 7 or 11 with this die are lower than with the fair one (15% with unfair die against 22% with fair die), so maybe it is not the best die to cheat the system :)
I'm having a big problem with multiplying the die-face values by the probabilities (36:50) to calculate the mean/expected value x • P(x). The values of the die faces shouldn't really carry a quantitative value; the faces could just as easily say "A," "B," "C," etc., or "blzje" and "tjwx" and "5 billion" or anything, really. They're merely labels. Why should "6" create the relatively "heavy" product .30, while "1" creates a product of only .05, when "6" and "1" carry exactly the same probabiility of being rolled? Something doesn't seem right there.
professor leonard, your way of teaching is quite simple and comprehensive. i am unable to view this video completely online as the screen goes green and it also shows error while downloading. could you please send me a link
I guess that negative probability might be if you roll a 1 and this always magically changes into some other number instead, or something like that. This would mean that even though you succeed with rolling a 1, that number still changes its mind and turns into something else.
+Yu m You've probably finished the class but in case anyone else would like to know I believe it's Introduction to Probability and Statistics- William Mendenhall- 14th edition
Professor Leonard, do you have an instructional video on Least Square Regression and Residuals? I take this class 1x a week and it just simply is not enough for me to get a grip! Your instructions/lectures are really helping me gain ground on this subject. I'm slightly panicking because I can't find anything and the book seems to be worthless! Boy, is this subject painful! :) Also, do you discuss using mean of y (critical value issue)?
Thank you Professor Leonard for sharing such informative and well-explained classes I have a question regarding the die probability distribution example where you have multiplied the value of each number that could appear with its probability to calculate the expected value. My question is, aren't the x(s) in this example are considered categorical data?
I have the same concern. I could not understand how that works when the numbers 1-6 in a die are simply categorical- nominal. Otherwise, great work, Dr. Leonard.
Thank you for posting your lectures, they are of great help! what book are you referring to when you mention chapter 5 and chapter 6? which statistics books do you recommend for clarity?
isnt the variance calculated by: the sum of (x-mean)squared multiplied by the probabilities? I get different values from the way i learn it in my statistics class
x^2 x P(x) = the 2nd moment of the random variable x = Expected value of x^2 and is noted E(x^2). The formula for Variance is E(x^2) - (E(x))^2. This is the 2nd moment minus the first moment squared.
First, thank you. You are an awesome teacher. You've got some lucky students! I do have a question though. Is there a specific reason u made a completely new x^2 column? Instead of just using column x and multiplying column xP (x) to get new column x^2P (x) ??? I hope you don't mind me asking. I'm taking an introductory statistics course this semester and I am usuing your videos as supplementary aids for content my class professor either loses me on or I just cant understands the way he explains it. BTW....just curious....ever think about moving to NC? :)
Dear Professor, It would have been mighty helpful if you would have explained the Variance formula, as in : in the formula ∑(x - µ)² * P(x) ---------------> WHY DO WE NEED TO MULTIPLY P(X) ? I GET ∑(x - µ)² IS THE FORMULA FOR VARIANCE. BUT IS THERE IS A WAY TO UNDERSTAND INTUITIVELY WHY {* P(X) }?
Mean from Prob distribution is interesting. When you multiply die numbers with probability, that;s where I am a little lost. What if the die didnt have numbers but colors (red,green,blue,yellow,green,cyan). How would we find x.P(x)
Colors are not random variables, so unless you can assign numbers to it, you cannot compute the mean and other statistics. For example, you can assign values from the frequency spectrum, then you'll be able to get some statistics about the color frequencies of your data. Or you play a game where some colors are more valuable than the others, then you order and enumerate them according to the order of importance. But what values you assign depends entirely on what problem you're trying to solve.
This is a great way to teach math. Too many professors rely on POWER POINTS with explanations and definitions and one example. That is an easy way out that offers very little learning. Math teachers need to be engaging and not drones! Great job Professor Leonard!
Exactly, they fail to make it make sense!
@@pabiedaisy8164 yho bro
Thanks to you I was able to take an entire statistics class in about a week -- and understand it. Incredible.
Am a student in Zambia, I never thought statistics would be this amazing till I came across Professor Leonard’s tutorials.
I am addict to your teaching now. I feel happy to think about to watch and learn. What a great teacher you are. I am so lucky to find these videos. May God always bless you with health, wealth and prosperity Ameen.
saima iram b
I actually enjoy watching these lectures and the sense of humor! they are such a help right now during online classes !
WOW! I'm speechless, what the heck did we study then this whole time? nothing..
That moment when your teachers suck.. I should've just watched these videos and never went to class..
Thanks for posting them!~
dear professor leonard,
i'm not sure if you're going to see this but i just want to say thank you from the bottom of my heart. a few years ago during the summer after freshman year of college, i was taking a calculus 3 class. i stumbled upon your videos and found them to be immensely helpful. once i finished the class, i thought i would never need your help again. well, here i am now. i'm a senior in college with just 1 more semester to go. i put off a statistics class because i was never good at probability & stats and i was afraid of it. once again, your videos have/are helping me. thank you so much. who knows when i will see you again.
So glad to have helped!! Best of luck in stats
I am a university student in Kenya, your lectures are very helpfu. Thank you....
I almost got my grade up to a C+ ever since I started binge watching Professor Leonards videos!
These lectures are extremely helpful. My prof teaches directly from r studio which is hard for me to understand. I truly appreciate this style of teaching.
This man got me through calc 3 and now he's saving my ass in stats. My professor is AWFUL!
My math teacher acted almost as if he was talking to himself or something.
He just stood there with a blank face and talked with a low monotonous voice - he didn't even show signs of annoyance or anything tangible like that, he was just on complete autopilot the whole time, like a robot.
He explains Stats so well.I go to class and then watch his videos as his way of teaching is so much better compared to my instructor.
You helped me so much with multivariable calculus and now you save my life in probability. THANK YOU!!
I have been struggling to wrap my head around discrete vs continuous for several days now. Your explanation made sense.
Your videos have saved my statistics grade! I wish I had found these before.
Thank you for sharing these videos! They have helped me out tremendously! Wish there were more professors like you to go around!
Just found your videos and they are helping me SO much!! I appreciate how thorough you are and how you break things down into simple English terms. Thankyou!!
You are literally making me fall inlove with stats at 2am in the morning. Thank you!
Thank you for still helping students worldwide, i found you through reddit suggestions from people across the globe. Who, like me, do NOT have the best professor..
Thank you! We just went over this section last week. I was confused, but this cleared things up. I'm going to do my homework and see how it goes.
Ok, I've been watching the videos from the start and someone (who I guess is the same person) keeps yawning in every single video. Please grab some coffee and focus on this awesome teacher!!
what an incredible teacher! Thank you for sharing and braking things down. My professors teach like we already know it. I swear my whole class is failing.
Why can't I get a teacher like this guy? I want to smack those kids who aren't paying attention to him.
me too
Like I said before, you're videos are amazing. You cover a lot of what's on my final exam for MA1670.
One of the best video on TH-cam I found it ever, it was very usefull for me thanks sir .I am from kashmir
Allow me to clarify the difference between discrete and continuous variables (or whatever else) a bit more clear and rigorously.:
A discrete variable can take only certain values AND no values IN BETWEEN. Like the set of Natural numbers or Integer numbers. Given two contiguous values, there is no value in between. Also, just like naturals and integers, their possible values could go up to infinity, no problem. And still be discrete.
A continuous variable can take infinite values as well, both positive and negative. However, given any two values, there are INFINITE values in between. And they are all valid. The set of real numbers is an example.
One could say the set of fractions or rational numbers can have infinite values in between. Yes. But the set of real numbers also include values that cannot be represented by a fraction, such as "pi" or "e", but that's a bit beside the point. However, it is relevant in the sense that the only set that is really continuous is the set of real numbers, including the aforementioned irrationals.
From this discussion it can be seen that the continuous vs. discrete random variables are actually based in number theory, in the sense that the same features seen in Integers and in Reals are the same characteristics between discrete and continuous random variables. Discrete values are a (sub)set of Integers, and continuous values belong to the (sub)set of Reals.
What is so difficult about explaining discrete vs continuous random variables in these terms? After all, statistics is solidly based in math. Let's use the tools that math already provide!
THANK YOU SO MUCH for sharing this. It helped me a ton with my online Stats course.
Your lectures are immensely helpful. Many thanks from Kenya
Back in the good ol' days. Man how time goes quick!
thank you prof. May this help my final examination. Keep on the good work
I am khursheed from kashmir......ur lectures r helpful
u r the best statistics teacher
I wanted to scream and tell your class that there has to be a whole 100%! 😆 (at around the 21min mark and I'm a ding dong in this. What I mean by that is you're doing the GREATEST job teaching me! Thank you!!!)
I personally thank for making me understand the probability distribution of how to to find the mean standard and variance.
you are truly a great professor , thank you so much , i am able to pass because of you. i wish i lived in America
this professor is amazing really
Thanks for the help!!!! My teacher never taught stats nearly this simple
Your teaching methods are just exemplary!! I don't understand the use of my college professors!
Wow!!! you're good...
I wish you were my Statistics Lecture :)
Your video was a great help..
Keep the good work up Sir ^_^
thank u so much!!!!!!! Tomorrow i have semester exam about Probabilty and statistics :) !!!!!!u r my source!!!! Thank u so much!!!!!!!!!!!!!! Leo :)
Modular class is so hard. Thanksto this.
Many thanks Professor , great work, am on distant PH , ur lectures really help me so much, be blessed
Professor, in 36:28 onwards, why did you multiply the number on the faces of the die and the probability?
Because he was finding the expected value. xP(x)
You're the best teacher I've ever seen! Where do you teach?
You explain everything which is great. Thank you
or we could just multiply the x column with the x.P(x) to get x^2.P(x), won't need the extra x^2 column :) , nice lecture
I wish I had your videos in my calculus 1 . you are the best professor. Thank you.
+abdi hashi he has calc 1 and calc 2 videos as well. Might want to check them out if you need those
+LoriliHime thanks .
Amazing teacher. Was able to make a B+ in my online course. And I suck at math
This is amazing. Thank you!
Stats online is convenient, but oh so painful..I’m basically trying to teach myself. :( Can’t thank you enough for these videos!!
Thank you Professor Leonard!
Thank you so much! Great explanation :)
Thank you Professor . This was really helpful .
4:19 Probability Distribution (Chart)
I strongly disagree with you on 40:16.
Expected value in general doesn't show which numbers are more frequent, the easiest way to see it is to compute an expectation for the fair die. All sides have probability 1/6, expectation is 3.5. Does that mean that most frequent sides are 3 and 4? Well, of course not, all sides are equally probable, you cannot pick any special side to be more frequent. I think of expectation in the following way: 'if you have the game where you accumulate points (our random variable) across multiple throws ( or experiments, if we're talking in general), the number of points that you'll get on average with k throws is equal to k multiplied by expectation'. So, saying that it shows most probable value is incorrect, it's the value you would kinda get in a long run.
Here's another example, let's assume that we have a three sided die with values 0, 100 and 10000 on the sides. The die is unfair, if falls on zero 98% of the time, 1% of the time on 100 and 1% of the time on 10000. If we compute mean for that die we will get 0*0.98+100*0.01+10000*0.01 = 101. Does that mean that 100 will be the most frequent value (as it is closest to the mean)? Well, certainly not 98% of the time it is.
Also one more thing to note, I think your chances of getting 7 or 11 with this die are lower than with the fair one (15% with unfair die against 22% with fair die), so maybe it is not the best die to cheat the system :)
I'm having a big problem with multiplying the die-face values by the probabilities (36:50) to calculate the mean/expected value x • P(x). The values of the die faces shouldn't really carry a quantitative value; the faces could just as easily say "A," "B," "C," etc., or "blzje" and "tjwx" and "5 billion" or anything, really. They're merely labels. Why should "6" create the relatively "heavy" product .30, while "1" creates a product of only .05, when "6" and "1" carry exactly the same probabiility of being rolled? Something doesn't seem right there.
Enjoyed the professor !
Fantastic presentation! Thank you! Helped tons.
Really helpful lecture
Great lesson, really helpful!
I usually like to think of the expected value as a scalar product.
Where was this man when I was in college 😩
What a handsome math teacher
Thank you so much!!!!! Very helpful
professor leonard, your way of teaching is quite simple and comprehensive. i am unable to view this video completely online as the screen goes green and it also shows error while downloading. could you please send me a link
these vids are great
I guess that negative probability might be if you roll a 1 and this always magically changes into some other number instead, or something like that.
This would mean that even though you succeed with rolling a 1, that number still changes its mind and turns into something else.
your a great professor. cannot stop mentioning you resemble Neil Patrick Harris on steroid.
I wonder which textbook you are using, this video has been a great help, thank you very much!
+Yu m You've probably finished the class but in case anyone else would like to know I believe it's Introduction to Probability and Statistics- William Mendenhall- 14th edition
so helpful, how did he end up getting the p(x)
Professor Leonard, do you have an instructional video on Least Square Regression and Residuals? I take this class 1x a week and it just simply is not enough for me to get a grip! Your instructions/lectures are really helping me gain ground on this subject. I'm slightly panicking because I can't find anything and the book seems to be worthless! Boy, is this subject painful! :) Also, do you discuss using mean of y (critical value issue)?
Thank you so much for this.
I really want to ask you my exercises questions =(((, you;re my life saver
Great professer...
please discuss what Bayes theorem is and where to apply it.
very helpfull guys, thanks a lot professor
Thank so much!!! Now I really understand
damn, he is good!
Many many thanks!
You are a COOL Professor.
I guess that what define random distribution is the moment: before the outcome is observed (occured).
Thank you sir
Thank you so much
Awesome✌
Thank you Professor Leonard for sharing such informative and well-explained classes
I have a question regarding the die probability distribution example where you have multiplied the value of each number that could appear with its probability to calculate the expected value. My question is, aren't the x(s) in this example are considered categorical data?
I have the same concern. I could not understand how that works when the numbers 1-6 in a die are simply categorical- nominal. Otherwise, great work, Dr. Leonard.
bless you
BOOKMARK:
left at 29:22
wish i had you as a professor!! :P
Thank you for posting your lectures, they are of great help! what book are you referring to when you mention chapter 5 and chapter 6? which statistics books do you recommend for clarity?
all lectures are named after chapters in "Triola, Elementary Statistics, 11th ed"
How to calculate P( exactly 501 Head)?
isnt the variance calculated by: the sum of (x-mean)squared multiplied by the probabilities? I get different values from the way i learn it in my statistics class
x^2 x P(x) = the 2nd moment of the random variable x = Expected value of x^2 and is noted E(x^2). The formula for Variance is E(x^2) - (E(x))^2. This is the 2nd moment minus the first moment squared.
First, thank you. You are an awesome teacher. You've got some lucky students!
I do have a question though. Is there a specific reason u made a completely new x^2 column? Instead of just using column x and multiplying column xP (x) to get new column x^2P (x) ???
I hope you don't mind me asking. I'm taking an introductory statistics course this semester and I am usuing your videos as supplementary aids for content my class professor either loses me on or I just cant understands the way he explains it.
BTW....just curious....ever think about moving to NC? :)
excellent sir
what if I dont have a P(X) value? The data are all random variables, how would I solve to get the probability of X?
So we know 1-6 are the variable of our DIE. How did we get the p(x): .05,.15,.35,.30,.10,.05. I can't seem to figure that out. Help!
He came up with his own probability.
why cant we use same standard deviation formuala "underroot sum (x-mean)^2/N" in probablity distribution method ??
Hi I am trying to find 5.1 and could not find it. Thanks for making this understandable.
this is 5.1
Dear Professor,
It would have been mighty helpful if you would have explained the Variance formula, as in :
in the formula ∑(x - µ)² * P(x) ---------------> WHY DO WE NEED TO MULTIPLY P(X) ?
I GET ∑(x - µ)² IS THE FORMULA FOR VARIANCE. BUT IS THERE IS A WAY TO UNDERSTAND INTUITIVELY WHY {* P(X) }?
shouldn't the variance = (summation of x.(Px) - mean)ˆ2 ??
Does anyone know what textbook is being used in this class? Introduction to Probability?
Mean from Prob distribution is interesting. When you multiply die numbers with probability, that;s where I am a little lost. What if the die didnt have numbers but colors (red,green,blue,yellow,green,cyan). How would we find x.P(x)
Colors are not random variables, so unless you can assign numbers to it, you cannot compute the mean and other statistics. For example, you can assign values from the frequency spectrum, then you'll be able to get some statistics about the color frequencies of your data. Or you play a game where some colors are more valuable than the others, then you order and enumerate them according to the order of importance. But what values you assign depends entirely on what problem you're trying to solve.
Hi. May I know why do you use the histogram for discrete data?