People keep saying that he is "over complicating" the content. However, the best way to study for a test for example is through complete understanding of what you are doing. Sal explains things in such detail in showing you WHERE equations and methods are derived from and WHY we are using them. With this understanding behind you, you are able to manipulate your knowledge for any question that you're hit with in an exam situation. THANK YOU SAL.
He mentions it quite often... maybe he should add to say: ms paint + a tablet (pc) and a pen + a screen capture software. With this 3 things you can make it like that.
after the change of indexes to a , b , it remains to show that the summation (15:00) = 1. this is easy to see by noting that this summation is the binomial expansion of (p + (1-p))^b ; ie 1^b
12:22 im confused here, why does (a+1) - (b+1) = a-b? why does he switch the b+1 to a b-1 and cancel them out (12:28)? surely n-k here would = a-b + 2?
Thanks for this explanation! I just missed a quick explanation on why you multiply by k inside the sum operator, but now I see it's because E(X) should return how many scores you make, so you sum every score possible, each skewed by it's own probability. E(X) = (0 scores)P(X=0) + (1 score)P(X=1) + ... + (n scores)P(X=n)
Expectation is the sum of every outcome times it’s probability. K is every outcome in range from 0 to n, and c(n,p)*p^k(1-p)^(n-k) is the probability X=k.
I have a doubt 15:02 - he takes the np out of the summation and says the summation is equal to 1 so E(X) = np but at 06:47 also we can take the K out of the summation and say that E(X)= K ??? Why
I think for 6:47, K are random variables, so their value are different and their probabilities are also different. For 15:02, n and p are just coefficients
This one took me a while, but I kept through it and it all made sense! Understanding the longer version of the probability formula took me forever but it was right in front of me lol. Just don't let all the variables intimidate you.
I have an exam and this has completely flipped and has completely confused me. It started great but I am trying to learn to solve these in a statistical formula and the easiest way to remember these.
I assumed it was a tablet aswell but I've thought about it and it can't be. Surely if it was the mouse pointer wouldn't move when he's not writing, no?
Is there a way to calculate probability of expected value? In our example expected value was 4 in 10shots which implies we are likely to score 4 in 10 shots but how likelt is it?
The expected outcome of an experiment involving any number of trials n, is directly proportional with the number of trials. If the expected value of 1 trial is 0,4 than the expected value of 10 trials is 4. If you have 40% chance of making the basket and you take 10 shots, then you'd expect to make 4 of those shots. You really can't perform infinty trials, but as you perform more and more trials the expected value is proportional to the number of trials. That's the way i understand it anyways.
Sounds very familiar to my professor. If we ask him a question he always looks at his notes handout that he distributes for every chapter and points to a formula. The visual aspect of it is much more helpful.
Hi Mr. Khan, I appreciate your effort for spreading knowledge throughout the world. Your videos helped me a lot to fill the gaps of my lack of knowledge. However, I would like to request you, if you kindly use different example other than basket ball, it would be even better to understand for students like me who are from outside USA. As the game is not so popular in our area, the rule of this game is completely unknown to me. Thank you.
At 11:30 you wrote in the denominator (n-k!) when that step you before that you had (n-k)! was that a mistake or is (n-k!) = (n-k)! btw thanks for the video.
I was a little confusing, in previous video "expected value", you said that expected value is some thing like the population mean. Due the population maybe infinite, so wecan not summarize all the numbers in population, we then calculate mean using x1*p(x1)+x2*p(x2)...., but here "Expected Value of Binomial Distribution" is np, how about n is infinite??
hey anyone wanna explain to me how i would put this equation into a calculator i know how to format it but i dont know how to solve. the thing that makes the least sense is the (n choose k)
in your calculator, u will see a key labelled nCr. that's ur combination key. always put the pick no first, press the shift bottom then nCr then press the smaller no last. e.g 5 chose 3 will be 5 nCr 3. press 5 then shift key, then nCr key, lastly key in 3. then the equal sign. and your answer is 10.
Hey Guys, help me out here! If you ask me the probability of making one shot, for me I would say p=30%. While saying this, I am actually providing an estimate that I'll be able to make 3 out of 10 shots for sure (means, P(X=3) given n=10 is 100%) But then using same numbers n=10 and p=3 I calculate the binomial probability of making 3 shots out of 10 and it is 26.68%!
![สาวเมืองเพชร - ธีเดช ทองอภิชาติ [Official MV]](http://i.ytimg.com/vi/kEt7F9PvO3I/mqdefault.jpg)
People keep saying that he is "over complicating" the content. However, the best way to study for a test for example is through complete understanding of what you are doing. Sal explains things in such detail in showing you WHERE equations and methods are derived from and WHY we are using them. With this understanding behind you, you are able to manipulate your knowledge for any question that you're hit with in an exam situation. THANK YOU SAL.
💯 In fact he explains in and out and “decomplicates”
Who else doing a whole semester of studying on the eve of their statistics final?
bobagopaaa
Good luck.
NexDemise hahaha just saw this...while cramming for my stats exam - hope you passed
who's not?
Lol I’m watching this in the beginning of class before the 2nd lecture
Midterm but same I guess
They need 4k remakes of these videos.
"My iPod wants to sync" Hilarious.
well you need to get a life @drew G.
"im talking about basketball not basket weaving.." LOL. And here I thought you were talking about probability of weaving a basket after doing shots :P
Prachi Singh oooh nooooo😜
Oh look at this! My iPod wants to sync.. he hee. I love this guy, he's doing such a great service to the field of education.. and so casually.
At 13:18, it should be np* Sum (from a=0 to b+1) not Sum (from a=0 to b)
He mentions it quite often... maybe he should add to say:
ms paint +
a tablet (pc) and a pen +
a screen capture software.
With this 3 things you can make it like that.
When final is 1 day ahead and realize that reading 350 pages is impossible.. AND suddenly this guy gives us perfect playlist
11:25 he messed up the factorial (n-k)!
Oh my god , statistics and math is magic !
Love it especially the last part where you say "E(X) = np for random variables whose probability distribution gives a binomial distribution"
this is so beautiful i could cry
At 12:34 you say...
n-k = a -b...
It seems like it should be...
n-k = b - a. Am I mistaken?
You are correct, well spotted. Another mistake is that a factorial inside a set of brackets when it shouldn't be at 11:25 .
wow this video explained it the best even after 12 years of its release,thanks sal
12:39 if a + 1 = k, b+1 = n then n - k = b+1 - a- 1 = b - a
dude I was like well this video looks old, then I see it's from 2009 and mind = blown lol, I thought khan academy was at most 5 years old.
after the change of indexes to a , b , it remains to show that the summation (15:00) = 1. this is easy to see by noting that this summation is the binomial expansion of (p + (1-p))^b ; ie 1^b
12:22 im confused here, why does (a+1) - (b+1) = a-b? why does he switch the b+1 to a b-1 and cancel them out (12:28)? surely n-k here would = a-b + 2?
Thanks for this explanation!
I just missed a quick explanation on why you multiply by k inside the sum operator, but now I see it's because E(X) should return how many scores you make, so you sum every score possible, each skewed by it's own probability.
E(X) = (0 scores)P(X=0) + (1 score)P(X=1) + ... + (n scores)P(X=n)
Expectation is the sum of every outcome times it’s probability. K is every outcome in range from 0 to n, and c(n,p)*p^k(1-p)^(n-k) is the probability X=k.
I have a doubt
15:02 - he takes the np out of the summation and says the summation is equal to 1 so E(X) = np
but at 06:47 also we can take the K out of the summation and say that E(X)= K ??? Why
I think for 6:47, K are random variables, so their value are different and their probabilities are also different. For 15:02, n and p are just coefficients
My God, he said it… 5:43
Extraordinary i am your fan .
6:50 sigma algebra
This one took me a while, but I kept through it and it all made sense! Understanding the longer version of the probability formula took me forever but it was right in front of me lol. Just don't let all the variables intimidate you.
I have an exam and this has completely flipped and has completely confused me. It started great but I am trying to learn to solve these in a statistical formula and the easiest way to remember these.
Man you are god🙂🙂🙂🙂
This is an awesome video! Dear video maker, you are a very talented teacher! :)
he is Khan himself, man
This is great explanation! thanks
Understood. Thanks
That was some seriously cool math you just did there! This is so helpful!!! THANK YOU!
Sir,give some problems we can solve
Thank you! I got to the derivation. Except I didn't know what to do with the summation!
It was really really great😍😍😭 thank you sooo much.
that's really cool!
Khan you are the best !
Mind blown,🤯
I enjoyed this, much better presented than my professor.
Amazing!!!
Elite thank u
Those videos are just great. Thank you Khan
Awesome explanation thank you!
Great. Tough but certainly enjoyable.
got it!! ....thank you sir.,.
You gotta love those last steps in a proof when everything just boils down to something very simple
At the end, it made sense. Thank you! That was a challenge.
So it Is basically like an average..at least in some cases...
I really enjoyed your prob and stat series. Would you please do a video on standard deviation for a binomial distribution.
Awesome sir, YOU are Really making concepts clear
Fabulous! You are amazing.
I assumed it was a tablet aswell but I've thought about it and it can't be. Surely if it was the mouse pointer wouldn't move when he's not writing, no?
Is there a way to calculate probability of expected value? In our example expected value was 4 in 10shots which implies we are likely to score 4 in 10 shots but how likelt is it?
Use formula: 10c4*(.4)^4*(.6)^6
you have very good & useful tutorials! many many thx for posting!
17 minutes to say E(X)= n•p 😂
Jokes aside, good explanation. √
periodt
why did we multiply by k at 6:23
Would help if you had a proof using the moment generating function too.
The expected outcome of an experiment involving any number of trials n, is directly proportional with the number of trials. If the expected value of 1 trial is 0,4 than the expected value of 10 trials is 4. If you have 40% chance of making the basket and you take 10 shots, then you'd expect to make 4 of those shots. You really can't perform infinty trials, but as you perform more and more trials the expected value is proportional to the number of trials. That's the way i understand it anyways.
Sounds very familiar to my professor. If we ask him a question he always looks at his notes handout that he distributes for every chapter and points to a formula. The visual aspect of it is much more helpful.
from this explanation can i say E(X)=K or K=np ?
I'm in probability and random variables right now. This is a common permutation formula in stats. The correct denominator is 'n!(n-k)!'.
Hi Mr. Khan, I appreciate your effort for spreading knowledge throughout the world. Your videos helped me a lot to fill the gaps of my lack of knowledge. However, I would like to request you, if you kindly use different example other than basket ball, it would be even better to understand for students like me who are from outside USA. As the game is not so popular in our area, the rule of this game is completely unknown to me. Thank you.
Excellent Understood it completely!
a wonderful proof!
Great job, well done...
It was very helpful. thank you.
(n-k!) should be (n-k)! In the denominator
Wow, great video
Best
YEAH!
Fantastic!
Thanks! ;)
Very nice!
In the first minute of the video, the mouse pointer was the one explaining the lesson.
6:49 'Some Sigma Algebra I guess you could call it' --- I see what you did there :D
He corrected at some later time :). Did you see the full video?
dude patrick what on the khan? i know its you man
Thank you man, you're a fucking genious
yes
Great video very good explanation...Little confusing but great effort..!!
Thank u very much,,!!
:P
he mentions it quite often, it's mspaint.exe
Your god!! Wooh!
At 11:30 you wrote in the denominator (n-k!) when that step you before that you had (n-k)! was that a mistake or is (n-k!) = (n-k)! btw thanks for the video.
It was a mistake!!
Replying to a 5 year old comment🤣😂🤣😂
Didn't understand the multiplying by K at 6.25
That's formula for Expectation
Never mind Sal. I see you corrected yourself around 14:00
Holy shieeet thank you Khan! You're a fookin genius, thank youu =)
G(old)
good! proof.
this isn`t a proof?
+Geekminer ur face is proof of gayness
市釧路
Have you seen my face?
I saw you while i was eating dinner at your house
its window paint. he says it in previous video. but i suspect that he has one of those pen pads for computer which helps him write properly
Neat
I was a little confusing, in previous video "expected value", you said that expected value is some thing like the population mean. Due the population maybe infinite, so wecan not summarize all the numbers in population, we then calculate mean using x1*p(x1)+x2*p(x2)...., but here "Expected Value of Binomial Distribution" is np, how about n is infinite??
this guy kinda sounds like job benjaminm from archer lol
hey anyone wanna explain to me how i would put this equation into a calculator i know how to format it but i dont know how to solve. the thing that makes the least sense is the (n choose k)
in your calculator, u will see a key labelled nCr.
that's ur combination key. always put the pick no first, press the shift bottom then nCr then press the smaller no last. e.g
5 chose 3 will be
5 nCr 3.
press 5 then shift key, then nCr key, lastly key in 3. then the equal sign.
and your answer is 10.
why 1?
I couldn't understand
Hey Guys, help me out here! If you ask me the probability of making one shot, for me I would say p=30%.
While saying this, I am actually providing an estimate that I'll be able to make 3 out of 10 shots for sure (means, P(X=3) given n=10 is 100%)
But then using same numbers n=10 and p=3 I calculate the binomial probability of making 3 shots out of 10 and it is 26.68%!
can anyone explain why p^k= p(p^k-1)?
Hi lets say k =2 so p^2 = p(p^2-1) or p^2 = p*p
toddy huang
p^k = p^k+1-1
p^k = p^1 * p^k-1
p^k = p(p^-1)
bc of
a^m+n = a^m * a^n
12: 32 - n-k should be b-a and not a-b
his handwriting thou...
It's from 2009 tho..
writing with a mouse is hard
This was way over complicated. Just substitute in your variables in to the formula and solve.
Your probability always adds up to 1.
You miss 100% of the shots you don't take.
please persian translate , thanks khan academy.
just scroll down enough and you'll be able to see our ancestors talking about Mspaint.exe and other ancient relics
as he taken n=b+1 ..then summation should be from a to b+1 not a to b...