My stat prof's teaching style just makes no sense at all and this guy helped me a lot. I got 86 in my first exam and 90 in my second exam just by watching this guy's videos. I didnt learn anything from my prof and the textbook. I should say thank you to you :D
Till 7:15 everything is explained great. The transition in Binomial Coefficients and the derivation of the formula for calculating Combinations (nCk) is a bit strange. Start with the definition of factorial: n! = 1.2.3...k...n, which describes in how many ways one can order/place n different items. To find in how many different ways we can draw (combine) k items from n, we need to get the k last numbers from n!, i.e. n.(n-1).(n-2)...k. This is done through a ratio, where the numerator is n! and the denominator is (n-k)!, i.e.: n! / (n-k)!. Because we don't care about the order of the drawn items (We don't care if we draw 1,2, 3; 1, 3, 2; or any of the other 4 possible ways. What matters is the numbers, not their position.), we additionally divide by k!, and finally we get: nCk = n! / k! (n-k)!
This is so helpful! My stat's prof spends almost 3 hours in class explaining things like this to us but because of his teaching style, it's hard for us to comprehend him. And if we enter it into a calculator without showing our work to prove we understand it, we can't get full credit on tests. So thank you! :)
guys the video is too much simple because it explains probability for high-school level or bachelor degree level..he is giving the basics with very simple notations..if you are a grad studies math student "like me" its better to follow MIT grad videos for complex problem solving..however these videos could help to refresh the basic old intuitions ..thank you khan for your great effort..
amazing......................... love the way you give the examples and explain the whole series is great .......... why don't we have teachers like you in colleges
I already did this material, but it was never explained why the binomial coefficient theorem works, we just crank out the formula. I assumed it must be a crazy proof, but your explanation is so succinct and straight-forward. Fantastic!
I guess that people who were familiar with the material beforehand understood Sal's video, but this was very difficult for me who is not familiar with the content he talks about...
Just to mention so that nobody gets confused.. if im not wrong, At about 09:35 P(x=1) should be 5! ÷ (3!×2!) ÷3! Instead of 5! ÷ (3!×3!) ÷3! His ultimate answer of 10 is correct nonetheless.
You did something wrong in the probability for x=3 ... It is correct that the result is 10/32 ... But you wrote the permutation as 5!/3!.3! And that wouldn't result the 10 ...
Thank you so much! Please keep up the good work! ))) And Hail you tube for providing space for such good videos. (Because think of it, only 15 years ago most pupils and students did not have access to such help. Now if you didn't understand something in class you can go to the web and fill in the blanks you have.
I'm sorry but I don't understand one step: P(X=2) -> we need to use the binomial coefficient so as said in the dedicated video (5 2) = 5!/(5-2)! So, here's my question: Why you are dividing by 2????
The example at 5:35, P(X=2). Seems like there would be only 4 possibilities for the first coin flip, for a chance of the fifth flip to be the 2nd flipped head P(X=2). The P solution still comes out the same tho. Anyways, this video is helping me a lot. Thank you Khan Academy
Bi-nominal Distribution explains the result of an experiment that has only two possible outcomes i.e. head/tale , accept/reject, pass/fail or yes/no etc. such an experiment is termed as the Bernoulli process.
youtube IS school. i dont mean that classroom teachers are bad (well some really are, like my schizophrenic physics teacher) but it is really HERE that we pay most attention because not because we're lazy, but because its the easiest source. shy people who dont ask questions can always replay doubtful parts and we can take all the time in the world to review the material in the video. in the end.......we should be grateful for being students in this golden age of technology.
If anyone is finding the math a lil confusing, here’s an equation I wrote up X = the number of times a thing happens after N number of rolls and a probability of c P(X=n)=N!/(n!(N-n)!)*c^n*(1-c)^(N-n)
Just a small note: on 12th minute and 15 sec, 5*4*3 can be written as 5!/2! and NOT 5!/3!. (Please note answer 5/16 to(5*4*3)/2! is correct) Thanks for your great lessons.
Can someone explain the "there's two ways this can happen" part which resulted in dividing by two? That part confused me. Is he saying because it can be any combo of Head 1 and Head 2 which leads to dividing by two?
This was confusing! Sounds like he did more telling than TEACHING.This is an intro to statistics playlist....this is all new to (most of) us. Like, what is a factorial??? He made this concept harder then it probably is. The previous videos were excellent tho!!
Confused all the things by saying the factorials. Simple you could have told P=(X=1)= 5 possibilities 5÷1 (chances of getting head) 5÷1=5 possibilities 1÷32=5÷32. P=(X=2)=5×4(1 and 2 possibility of getting 2 heads in 5 flips) 20÷2=10 then 10÷32=5÷16. P=(X=3)=5*4*3( getting the chances of heads of 3 in 5 flips) 5*4*3÷3*2*1=10=10÷32=5÷16. Don't get confused write it in the factorials form while he teaching you will get to know
@someones1 its not his fault , probability theory always sucks . if i hear the phrase" flip a coin" one more time ,the probability of me having a nervous breakdown =1
For the probability that two heads are flipped, why are there 5 possible places for the first head? If it's in the fifth position then there is no more room for a second head flip.
Am I the only one who feels like he over-explains and him making these small mistakes and stammering here and there kinda throws you back a little and makes you more confused? I feel like the only way you can understand any of this fully is to know everything beforehand.
I kinda agree with you...He was really fast at some points...and at around 4:39 he was talking about chairs....I got totally lost...but I feel I gained something.
Noshin Saiyara This is probably way too late, but what I do when that happens, is to take notes of everything new information he says. Then you won't be confused by him saying the same thing over and over again.
My stat prof's teaching style just makes no sense at all and this guy helped me a lot. I got 86 in my first exam and 90 in my second exam just by watching this guy's videos. I didnt learn anything from my prof and the textbook. I should say thank you to you :D
Almost 6 years ago...
Did statistics help you to find a well-paid job?I think it did
where are you now?
you just forget to mention this formula: n!/x!(n-x)!
I think thats why people are getting confuse
ohhh i see.
everyone needs to big up this comment cause it saved my life
hero
Till 7:15 everything is explained great. The transition in Binomial Coefficients and the derivation of the formula for calculating Combinations (nCk) is a bit strange.
Start with the definition of factorial: n! = 1.2.3...k...n, which describes in how many ways one can order/place n different items.
To find in how many different ways we can draw (combine) k items from n, we need to get the k last numbers from n!, i.e. n.(n-1).(n-2)...k. This is done through a ratio, where the numerator is n! and the denominator is (n-k)!, i.e.: n! / (n-k)!.
Because we don't care about the order of the drawn items (We don't care if we draw 1,2, 3; 1, 3, 2; or any of the other 4 possible ways. What matters is the numbers, not their position.), we additionally divide by k!, and finally we get: nCk = n! / k! (n-k)!
I think sal, in the 3 heads case it should read as
P(X=3)= 5!/(3!2!)
because you solved it like above but written it as
P(X=3)= 5!/(3!3!)
Theuna Hime I thought so too!
yes, if you put it in the formula of combination n choose r
thanks for your comment I got confused toohere
Yes it should be 5!/(3!2!)
It make more sense for those who knows Permutations and Combinations
Because that is just 5C2.
And nCr = n!/[r! (n-r)!]
This is so helpful! My stat's prof spends almost 3 hours in class explaining things like this to us but because of his teaching style, it's hard for us to comprehend him. And if we enter it into a calculator without showing our work to prove we understand it, we can't get full credit on tests. So thank you! :)
guys the video is too much simple because it explains probability for high-school level or bachelor degree level..he is giving the basics with very simple notations..if you are a grad studies math student "like me" its better to follow MIT grad videos for complex problem solving..however these videos could help to refresh the basic old intuitions ..thank you khan for your great effort..
Doaa Serageldin can you please attach a link for MIT grad videos
10:06 shouldn't it be 5!/2!3!?
amazing.........................
love the way you give the examples and explain
the whole series is great ..........
why don't we have teachers like you in colleges
I already did this material, but it was never explained why the binomial coefficient theorem works, we just crank out the formula. I assumed it must be a crazy proof, but your explanation is so succinct and straight-forward. Fantastic!
I guess that people who were familiar with the material beforehand understood Sal's video, but this was very difficult for me who is not familiar with the content he talks about...
I believe at 9:33 there is an errata: Sal has mentioned
P(X=3)= 5!/(3!3!)
However: it should be: P(X=3)= 5!/(3!2!)
10:05 He wrote it wrong, should be:
(5!)/((3!)(2!)) for P(X=3)
Thanks for pointing that out. I made an annotation.
Just to mention so that nobody gets confused.. if im not wrong,
At about 09:35
P(x=1) should be 5! ÷ (3!×2!) ÷3!
Instead of 5! ÷ (3!×3!) ÷3!
His ultimate answer of 10 is correct nonetheless.
There is a difference with flipping five coins at once, at flipping one coin 5 times. The five coins interact with each other.
P(X = 3), but yes, as the annotation says, it should be 3!2! on the denominator at 9:35
It is P(X=3)
He is the smartest man alive.
This guy will one day win the Nobel peace prize - for changing millions of fates for the better!
I APPRECIATE THAT YOU TAKE THE TIME TO MAKE THESE VIDEOS FOR ALL OF US
Thanks for explaining binomial distributions, much easier than my stats classes!
You did something wrong in the probability for x=3 ... It is correct that the result is 10/32 ... But you wrote the permutation as 5!/3!.3! And that wouldn't result the 10 ...
this is my third time of watching. Now I get it! Always seems obvious in hindsight
Thank you so much! Please keep up the good work! )))
And Hail you tube for providing space for such good videos. (Because think of it, only 15 years ago most pupils and students did not have access to such help. Now if you didn't understand something in class you can go to the web and fill in the blanks you have.
any chance you will redo the old vids since they are a bit pixelated?
really?
I owe my grades to you Mr. Khan. Thank you for teaching me in 10 minutes what my teacher takes 55 minutes to teach.
I'm sorry but I don't understand one step:
P(X=2) -> we need to use the binomial coefficient so as said in the dedicated video (5 2) = 5!/(5-2)!
So, here's my question: Why you are dividing by 2????
thank GOD for people who can actually explain math well....
This is how I learn what i do in Ap Stat every day. WAY better than my teacher!
@10:05 Please correct it , should be:
(5!)/((3!)(2!)) for P(X=3)
The example at 5:35, P(X=2). Seems like there would be only 4 possibilities for the first coin flip, for a chance of the fifth flip to be the 2nd flipped head P(X=2). The P solution still comes out the same tho. Anyways, this video is helping me a lot. Thank you Khan Academy
Learn permutation and combination master it this will seem easy to u.
At 9:30-9:35, 5×4×3 does not = 5 factorial ÷ 3 factorial. 5 factorial ÷ 3 factoial = 5×4, which = 20.
you are better than wikipedia AND my statistics teacher
Bi-nominal Distribution explains the result of an experiment that has only two possible outcomes i.e. head/tale , accept/reject, pass/fail or yes/no etc. such an experiment is termed as the Bernoulli process.
youtube IS school. i dont mean that classroom teachers are bad (well some really are, like my schizophrenic physics teacher) but it is really HERE that we pay most attention because not because we're lazy, but because its the easiest source. shy people who dont ask questions can always replay doubtful parts and we can take all the time in the world to review the material in the video.
in the end.......we should be grateful for being students in this golden age of technology.
Thank's so much for generously giving us your time and explaining things so thoroughly.
Good video, I learned a lot from it. Please note: (5x4x3)/3! = 10 and 5!/(3!x3!) = 10/3.
0:40 ensemble statistics & time statistics
Thank you very much... you saved me from failure
Thanks for the videos. It helped me understand some of these subjects much better. I will definitely watch your other videos as well.
If anyone is finding the math a lil confusing, here’s an equation I wrote up
X = the number of times a thing happens after N number of rolls and a probability of c
P(X=n)=N!/(n!(N-n)!)*c^n*(1-c)^(N-n)
Thanks so muchh! great review for the ap stats exam tomorrow(:
typo at 9:52 instead of 5!/3!3! it should be 5!/3!2! because the formula n!/(n-k)! is 5-3 = 2! and so it still equals 10
Just a small note:
on 12th minute and 15 sec, 5*4*3 can be written as 5!/2! and NOT 5!/3!. (Please note answer 5/16 to(5*4*3)/2! is correct)
Thanks for your great lessons.
@9:35 should be 5! / ( 3! * 2!)
where the 2! came from (5-3)!
Damn these older videos are hard to watch haha.
Anon Ymous i know right lol
You get used to it after a while xD
thanks a lot. It is very helpful
Can someone explain the "there's two ways this can happen" part which resulted in dividing by two? That part confused me. Is he saying because it can be any combo of Head 1 and Head 2 which leads to dividing by two?
Well explained! Thank you!
This was the most complicated way I’ve ever seen this explained but after knowing the basic explanation I supposed this helped?
Actually wait jk, this just confuses me a little more
Thanks a lot mr khan, more power!
Well this just halved my Stats revision time
so damn inuitive, maybe the most straight forward math since grade school....
thank you for confusing me even more
I agree absolutely.Check Leonard statistics lectures, which make you understand easily....lol
At 9:30-9:35, 5×4×3 does not = 5 factorial ÷ 3 factorial. 5 factorial ÷ 3 factorial = 5×4, which = 20.
This was a little confusing
At 9:30-9:35, 5×4×3 does not = 5 factorial ÷ 3 factorial. 5 factorial ÷ 3 factorial = 5×4, which = 20.
+Kenny Allison where you are read
No. It was not.
yes.....he over explained
Nobel prize for Sal Khan
jesus christ that's a brutal explanation!!!!
Please advise should P(X=3) be 20 * 1/32 ?????
i hope i would pass in this exam by watching this video.
This lesson will be confusing if you don't have knowledge of combinatorics (Basic counting principles: selections/permutations)
OMG = John Mayer teaches the binomial distribution!!!
so no head? 1:24
that is a great shortcut
This was confusing! Sounds like he did more telling than TEACHING.This is an intro to statistics playlist....this is all new to (most of) us. Like, what is a factorial??? He made this concept harder then it probably is. The previous videos were excellent tho!!
I need to find a video on finding specific terms in binomial expansions - does anyone know where I can find one?
Why was P=(X=3)
5x4x3
---------
3!
And not
5x4x3
--------
3
Thanks!
at 10:00 shouldnt it be 5!/3!*2! which is why they are the same
Thank you very much!
Confused all the things by saying the factorials.
Simple you could have told
P=(X=1)= 5 possibilities 5÷1 (chances of getting head) 5÷1=5 possibilities 1÷32=5÷32.
P=(X=2)=5×4(1 and 2 possibility of getting 2 heads in 5 flips) 20÷2=10 then 10÷32=5÷16.
P=(X=3)=5*4*3( getting the chances of heads of 3 in 5 flips) 5*4*3÷3*2*1=10=10÷32=5÷16.
Don't get confused write it in the factorials form while he teaching you will get to know
Thank you!
Hats off!!!
Why only the p(x=2 )only having 2! and the others not having them ?The others no need to be divided by 2 ?
Thanks bro.
anybody knows why was it a combination not permutation? I thought the order did matter...
@dAvrilthebear yes sir. we have an additional resource that students of the past do not have
Could you remake these videos?
shy people can ask questions in the comment section, too.
@someones1 its not his fault , probability theory always sucks .
if i hear the phrase" flip a coin" one more time ,the probability of me having a nervous breakdown =1
i'll second that!!!
thank you sooooooooo much!!!!!!!!!!!!!!!!!
probexpectation =
((number of throws)!/((number of expecation)!*(numberof throws - number of expectation)!)*probabilityofcase*numberofthrows
thanks a lot.............
why divided by 2?
Thanks sal
yes we khan
huh, what do you mean?
he's dividing by x =2
thank you :-)
240p?
Fair enough! :)
Better than Wikipedia? I don't know...that's a close one.
Heading is different and video is different. confusing.
@shantanudas if obama could get one Khan should get 5 of them
Is this man Eli the computer guy..??
So confusing, any other way to explin
i pity people's current stats teacher
For the probability that two heads are flipped, why are there 5 possible places for the first head? If it's in the fifth position then there is no more room for a second head flip.
woow
or 50%
Am I the only one who feels like he over-explains and him making these small mistakes and stammering here and there kinda throws you back a little and makes you more confused? I feel like the only way you can understand any of this fully is to know everything beforehand.
I kinda agree with you...He was really fast at some points...and at around 4:39 he was talking about chairs....I got totally lost...but I feel I gained something.
Yes, yes you are.
Noshin Saiyara This is probably way too late, but what I do when that happens, is to take notes of everything new information he says. Then you won't be confused by him saying the same thing over and over again.
It wasn't his best showing.
wooo
09:11 Does NOT sum up Khan's approach to maths.
For all Germans : Unser k(Anzahl der Treffer)) ist hier n. n ist nicht die kettenlänge !