Expected value of binomial distribution | Probability and Statistics | Khan Academy

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  • เผยแพร่เมื่อ 1 ก.พ. 2025

ความคิดเห็น • 133

  • @danielacalvani7251
    @danielacalvani7251 7 ปีที่แล้ว +130

    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.

    • @kalanakavishanka3152
      @kalanakavishanka3152 10 หลายเดือนก่อน +2

      💯 In fact he explains in and out and “decomplicates”

  • @NexDemise
    @NexDemise 10 ปีที่แล้ว +359

    Who else doing a whole semester of studying on the eve of their statistics final?

    • @NexDemise
      @NexDemise 8 ปีที่แล้ว +1

      bobagopaaa
      Good luck.

    • @kitiarian4371
      @kitiarian4371 7 ปีที่แล้ว +5

      NexDemise hahaha just saw this...while cramming for my stats exam - hope you passed

    • @shamofengbao
      @shamofengbao 7 ปีที่แล้ว +3

      who's not?

    • @MrTimmy23
      @MrTimmy23 6 ปีที่แล้ว +2

      Lol I’m watching this in the beginning of class before the 2nd lecture

    • @mika2666
      @mika2666 5 ปีที่แล้ว +4

      Midterm but same I guess

  • @mayurkarnik
    @mayurkarnik 13 ปีที่แล้ว +3

    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.

  • @PrachiSingh-et3kz
    @PrachiSingh-et3kz 10 ปีที่แล้ว +59

    "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

    • @isaacjilo1560
      @isaacjilo1560 5 ปีที่แล้ว

      Prachi Singh oooh nooooo😜

  • @chrisray9653
    @chrisray9653 4 ปีที่แล้ว +10

    They need 4k remakes of these videos.

  • @cococnk388
    @cococnk388 2 ปีที่แล้ว +1

    Love it especially the last part where you say "E(X) = np for random variables whose probability distribution gives a binomial distribution"

  • @drewg.3049
    @drewg.3049 7 ปีที่แล้ว +39

    "My iPod wants to sync" Hilarious.

    • @therealilyaskhan
      @therealilyaskhan 6 ปีที่แล้ว +1

      well you need to get a life @drew G.

  • @zhouyinwei2007
    @zhouyinwei2007 4 ปีที่แล้ว +1

    Oh my god , statistics and math is magic !

  • @tanayasharma7776
    @tanayasharma7776 3 ปีที่แล้ว +1

    wow this video explained it the best even after 12 years of its release,thanks sal

  • @judahdsouza9196
    @judahdsouza9196 4 ปีที่แล้ว +3

    this is so beautiful i could cry

  • @norwayte
    @norwayte 16 ปีที่แล้ว +3

    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.

  • @GiorgiVardi
    @GiorgiVardi 6 ปีที่แล้ว +11

    When final is 1 day ahead and realize that reading 350 pages is impossible.. AND suddenly this guy gives us perfect playlist

  • @swfsql
    @swfsql ปีที่แล้ว

    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)

    • @freeman5860
      @freeman5860 ปีที่แล้ว

      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.

  • @pawxgamingmario9813
    @pawxgamingmario9813 2 หลายเดือนก่อน +2

    My God, he said it… 5:43

  • @CreepypastaFiles
    @CreepypastaFiles 12 ปีที่แล้ว +2

    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.

  • @DeshantaDevkota
    @DeshantaDevkota 4 ปีที่แล้ว +2

    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.

  • @brianlewis703
    @brianlewis703 7 ปีที่แล้ว +1

    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

  • @linwang1337
    @linwang1337 7 ปีที่แล้ว +3

    At 13:18, it should be np* Sum (from a=0 to b+1) not Sum (from a=0 to b)

  • @sleephourofmotivatwakeupas6512
    @sleephourofmotivatwakeupas6512 6 ปีที่แล้ว +1

    Man you are god🙂🙂🙂🙂

  • @himanshukashyap1654
    @himanshukashyap1654 5 ปีที่แล้ว +2

    Extraordinary i am your fan .

  • @blazcukelj7273
    @blazcukelj7273 2 ปีที่แล้ว

    This is great explanation! thanks

  • @kovoliver
    @kovoliver 8 ปีที่แล้ว +9

    This is an awesome video! Dear video maker, you are a very talented teacher! :)

    • @tizzavo
      @tizzavo 7 ปีที่แล้ว +4

      he is Khan himself, man

  • @Mau365PP
    @Mau365PP 6 ปีที่แล้ว +6

    11:25 he messed up the factorial (n-k)!

  • @ElvinJones1981
    @ElvinJones1981 10 ปีที่แล้ว +22

    At 12:34 you say...
    n-k = a -b...
    It seems like it should be...
    n-k = b - a. Am I mistaken?

    • @edwarddurrans8489
      @edwarddurrans8489 10 ปีที่แล้ว +8

      You are correct, well spotted. Another mistake is that a factorial inside a set of brackets when it shouldn't be at 11:25 .

  • @mahirhasan9212
    @mahirhasan9212 3 ปีที่แล้ว

    Mind blown,🤯

  • @kotharigaurav1354
    @kotharigaurav1354 3 ปีที่แล้ว

    Understood. Thanks

  • @inxeoz
    @inxeoz 4 หลายเดือนก่อน

    12:39 if a + 1 = k, b+1 = n then n - k = b+1 - a- 1 = b - a

  • @andrewlace55
    @andrewlace55 11 ปีที่แล้ว +1

    I enjoyed this, much better presented than my professor.

  • @dianasci
    @dianasci 4 ปีที่แล้ว

    It was really really great😍😍😭 thank you sooo much.

  • @savannahwoodard6441
    @savannahwoodard6441 3 ปีที่แล้ว

    That was some seriously cool math you just did there! This is so helpful!!! THANK YOU!

  • @mrkotfw
    @mrkotfw 13 ปีที่แล้ว

    Thank you! I got to the derivation. Except I didn't know what to do with the summation!

  • @heathersmith4015
    @heathersmith4015 2 ปีที่แล้ว +1

    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.

  • @amintalukder7189
    @amintalukder7189 6 ปีที่แล้ว

    Khan you are the best !

  • @OmerCelik-ku8ot
    @OmerCelik-ku8ot 3 หลายเดือนก่อน +1

    6:50 sigma algebra

  • @rohitashvaraj8399
    @rohitashvaraj8399 5 ปีที่แล้ว +1

    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

    • @kimhormong
      @kimhormong 4 ปีที่แล้ว

      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

  • @JosephMill
    @JosephMill ปีที่แล้ว

    Elite thank u

  • @nicolatesla2
    @nicolatesla2 10 ปีที่แล้ว +1

    Those videos are just great. Thank you Khan

  • @drmugtaba
    @drmugtaba 13 ปีที่แล้ว

    Great. Tough but certainly enjoyable.

  • @bruh_5555
    @bruh_5555 2 ปีที่แล้ว

    Amazing!!!

  • @bigsmerdo
    @bigsmerdo ปีที่แล้ว

    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?

  • @KYChen617
    @KYChen617 4 ปีที่แล้ว

    Awesome explanation thank you!

  • @eyad_aiman
    @eyad_aiman 3 ปีที่แล้ว

    that's really cool!

  • @cktailor
    @cktailor 11 ปีที่แล้ว

    I'm in probability and random variables right now. This is a common permutation formula in stats. The correct denominator is 'n!(n-k)!'.

  • @subhamaykoley1757
    @subhamaykoley1757 4 ปีที่แล้ว +1

    Sir,give some problems we can solve

  • @tharunishadi3980
    @tharunishadi3980 12 ปีที่แล้ว

    got it!! ....thank you sir.,.

  • @rafaelaprende
    @rafaelaprende 10 ปีที่แล้ว +1

    At the end, it made sense. Thank you! That was a challenge.

  • @shazaduh
    @shazaduh 15 ปีที่แล้ว

    I really enjoyed your prob and stat series. Would you please do a video on standard deviation for a binomial distribution.

  • @cktailor
    @cktailor 11 ปีที่แล้ว

    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.

  • @davidb1286
    @davidb1286 14 ปีที่แล้ว

    Would help if you had a proof using the moment generating function too.

  • @MegaMuffinManX
    @MegaMuffinManX 14 ปีที่แล้ว

    You gotta love those last steps in a proof when everything just boils down to something very simple

  • @BARaaz04
    @BARaaz04 7 ปีที่แล้ว

    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.

  • @mortenrobinson
    @mortenrobinson 12 ปีที่แล้ว +1

    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.

  • @SooperMablo
    @SooperMablo 14 ปีที่แล้ว

    Fabulous! You are amazing.

  • @jshuacc
    @jshuacc 15 ปีที่แล้ว

    you have very good & useful tutorials! many many thx for posting!

  • @leif1075
    @leif1075 5 ปีที่แล้ว +1

    So it Is basically like an average..at least in some cases...

  • @pavanmachavarapu9999
    @pavanmachavarapu9999 5 ปีที่แล้ว

    Awesome sir, YOU are Really making concepts clear

  • @haneulkim4902
    @haneulkim4902 4 ปีที่แล้ว

    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?

  • @ROXcursed
    @ROXcursed 16 ปีที่แล้ว

    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?

  • @alphasoftwaresolutions8977
    @alphasoftwaresolutions8977 7 ปีที่แล้ว

    from this explanation can i say E(X)=K or K=np ?

  • @0ijm3409fiwrekj
    @0ijm3409fiwrekj 11 ปีที่แล้ว

    Excellent Understood it completely!

  • @adnanul-hasan3096
    @adnanul-hasan3096 12 ปีที่แล้ว

    He corrected at some later time :). Did you see the full video?

  • @kmdarie
    @kmdarie 8 ปีที่แล้ว +2

    a wonderful proof!

  • @mollzz
    @mollzz 14 ปีที่แล้ว

    Wow, great video

  • @colmdube
    @colmdube 9 ปีที่แล้ว

    Great job, well done...

  • @philipschloesser
    @philipschloesser 7 ปีที่แล้ว

    6:49 'Some Sigma Algebra I guess you could call it' --- I see what you did there :D

  • @FEFRANKIE
    @FEFRANKIE 11 ปีที่แล้ว

    It was very helpful. thank you.

  • @NotMadeOfManitobaFlour
    @NotMadeOfManitobaFlour 4 ปีที่แล้ว +2

    17 minutes to say E(X)= n•p 😂
    Jokes aside, good explanation. √

  • @paulceltics
    @paulceltics 13 ปีที่แล้ว

    yes

  • @jonyb0b13
    @jonyb0b13 11 ปีที่แล้ว +1

    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.

    • @RuinsOfTheUnknown
      @RuinsOfTheUnknown 5 ปีที่แล้ว +1

      It was a mistake!!
      Replying to a 5 year old comment🤣😂🤣😂

  • @niconikko
    @niconikko 13 ปีที่แล้ว

    In the first minute of the video, the mouse pointer was the one explaining the lesson.

  • @supermario_49
    @supermario_49 6 ปีที่แล้ว +1

    (n-k!) should be (n-k)! In the denominator

  • @inDiSTruCtiBleJoHn
    @inDiSTruCtiBleJoHn 13 ปีที่แล้ว

    YEAH!
    Fantastic!
    Thanks! ;)

  • @balakumaranm4499
    @balakumaranm4499 4 ปีที่แล้ว

    Best

  • @srividyapratha9053
    @srividyapratha9053 6 ปีที่แล้ว

    why did we multiply by k at 6:23

  • @Vupadhayay
    @Vupadhayay 13 ปีที่แล้ว

    Great video very good explanation...Little confusing but great effort..!!
    Thank u very much,,!!
    :P

  • @zenontaoushianis8771
    @zenontaoushianis8771 10 ปีที่แล้ว

    Very nice!

  • @heyyhowyadoin
    @heyyhowyadoin 13 ปีที่แล้ว +1

    dude patrick what on the khan? i know its you man

  • @hawkister
    @hawkister 15 ปีที่แล้ว

    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

  • @Incrue
    @Incrue 9 ปีที่แล้ว +1

    Thank you man, you're a fucking genious

  • @BlahBlah7151
    @BlahBlah7151 14 ปีที่แล้ว

    Your god!! Wooh!

  • @TMCP-l4h
    @TMCP-l4h 10 ปีที่แล้ว

    good! proof.

    • @The112Windows
      @The112Windows 10 ปีที่แล้ว

      this isn`t a proof?

    • @Kevin-iu4kj
      @Kevin-iu4kj 9 ปีที่แล้ว +1

      +Geekminer ur face is proof of gayness

    • @The112Windows
      @The112Windows 9 ปีที่แล้ว

      市釧路
      Have you seen my face?

    • @Kevin-iu4kj
      @Kevin-iu4kj 9 ปีที่แล้ว

      I saw you while i was eating dinner at your house

  • @dtletmedn
    @dtletmedn 12 ปีที่แล้ว

    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??

  • @ElvinJones1981
    @ElvinJones1981 10 ปีที่แล้ว

    Never mind Sal. I see you corrected yourself around 14:00

  • @armaanoo
    @armaanoo 8 ปีที่แล้ว

    12: 32 - n-k should be b-a and not a-b

  • @anindyapatowary3469
    @anindyapatowary3469 6 ปีที่แล้ว

    Didn't understand the multiplying by K at 6.25

  • @abual-khwarizmi6103
    @abual-khwarizmi6103 9 ปีที่แล้ว +1

    Holy shieeet thank you Khan! You're a fookin genius, thank youu =)

  • @lvecsey
    @lvecsey 16 ปีที่แล้ว +1

    he mentions it quite often, it's mspaint.exe

  • @Utkarshkharb
    @Utkarshkharb 4 ปีที่แล้ว

    G(old)

  • @Artifactorfiction
    @Artifactorfiction 10 ปีที่แล้ว

    Neat

  • @bubblewrap55
    @bubblewrap55 8 ปีที่แล้ว +1

    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%!

  • @adarshgaurav2078
    @adarshgaurav2078 7 ปีที่แล้ว

    as he taken n=b+1 ..then summation should be from a to b+1 not a to b...

  • @apleseed91
    @apleseed91 13 ปีที่แล้ว

    this guy kinda sounds like job benjaminm from archer lol

  • @hung89341
    @hung89341 8 ปีที่แล้ว +2

    can anyone explain why p^k= p(p^k-1)?

    • @jayantliving
      @jayantliving 8 ปีที่แล้ว +1

      Hi lets say k =2 so p^2 = p(p^2-1) or p^2 = p*p

    • @koshaboi619
      @koshaboi619 8 ปีที่แล้ว +1

      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

  • @alyssahohoho2646
    @alyssahohoho2646 8 ปีที่แล้ว +1

    his handwriting thou...

    • @trapis03
      @trapis03 8 ปีที่แล้ว +2

      It's from 2009 tho..

    • @czJanKrejci
      @czJanKrejci 6 ปีที่แล้ว +1

      writing with a mouse is hard

  • @raquelconceicao
    @raquelconceicao 8 ปีที่แล้ว +1

    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)

    • @k2d10tode11
      @k2d10tode11 7 ปีที่แล้ว +1

      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.

  • @hesamjalali9183
    @hesamjalali9183 7 ปีที่แล้ว

    please persian translate , thanks khan academy.

  • @Ny_babs
    @Ny_babs 7 ปีที่แล้ว +2

    This was way over complicated. Just substitute in your variables in to the formula and solve.
    Your probability always adds up to 1.

  • @mainakdeb9188
    @mainakdeb9188 7 ปีที่แล้ว

    just scroll down enough and you'll be able to see our ancestors talking about Mspaint.exe and other ancient relics

  • @aliminhaz9909
    @aliminhaz9909 8 ปีที่แล้ว +1

    why 1?
    I couldn't understand

  • @edwardsu764
    @edwardsu764 3 ปีที่แล้ว

    You miss 100% of the shots you don't take.