I think the order in the "Probability Distributions" is reversed, this should come before the Binomial, right? Thanks, loving these, extremely helpful and concise.
2:15 I have seeking the steps before variance standard formula jumping into p(1-p) … does anyone know the missing parts. Really wanna know what’s the middle steps.. otherwise I had to hard code in my memory
The variance of a Bernoulli distributed X {\displaystyle X} is Var [ X ] = p q = p ( 1 − p ) {\displaystyle \operatorname {Var} [X]=pq=p(1-p)} We first find E [ X 2 ] = Pr ( X = 1 ) ⋅ 1 2 + Pr ( X = 0 ) ⋅ 0 2 = p ⋅ 1 2 + q ⋅ 0 2 = p = E [ X ] {\displaystyle \operatorname {E} [X^{2}]=\Pr(X=1)\cdot 1^{2}+\Pr(X=0)\cdot 0^{2}=p\cdot 1^{2}+q\cdot 0^{2}=p=\operatorname {E} [X]} From this follows Var [ X ] = E [ X 2 ] − E [ X ] 2 = E [ X ] − E [ X ] 2 = p − p 2 = p ( 1 − p ) = p q {\displaystyle \operatorname {Var} [X]=\operatorname {E} [X^{2}]-\operatorname {E} [X]^{2}=\operatorname {E} [X]-\operatorname {E} [X]^{2}=p-p^{2}=p(1-p)=pq}[3] With this result it is easy to prove that, for any Bernoulli distribution, its variance will have a value inside [ 0 , 1 / 4 ] {\displaystyle [0,1/4]}.
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Dunya ve hayat.
Short and informative. Channel subscribed
by far this video is the best I have seen on Brn (P). I am going to check his other videos. Thank you very much.
Very good illustration....!
The examples are easy yet do not loose the essence of the topic
So basically, its an elementary case of a binomial distribution?
Great video! Thanks, 365!
I think the order in the "Probability Distributions" is reversed, this should come before the Binomial, right? Thanks, loving these, extremely helpful and concise.
Who is the evil soul that disliked such an excellent video
23 people failed high school math
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Thank you
Can you tell in which of the branches of engineering probability and binomial distribution used
in 2:22 how to get the second line? like the values of x0- miu and then (0-p)^2 I didn't get that
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How to calculate mode and median for this distribution?
Why variance is not equal to p . (1 - p)^2 ??
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For a Bernoulli r.v.x, μ3=0.7 what is Var( X) ?
Good deal!
2:15 I have seeking the steps before variance standard formula jumping into p(1-p) … does anyone know the missing parts. Really wanna know what’s the middle steps.. otherwise I had to hard code in my memory
The variance of a Bernoulli distributed X {\displaystyle X} is
Var [ X ] = p q = p ( 1 − p ) {\displaystyle \operatorname {Var} [X]=pq=p(1-p)}
We first find
E [ X 2 ] = Pr ( X = 1 ) ⋅ 1 2 + Pr ( X = 0 ) ⋅ 0 2 = p ⋅ 1 2 + q ⋅ 0 2 = p = E [ X ] {\displaystyle \operatorname {E} [X^{2}]=\Pr(X=1)\cdot 1^{2}+\Pr(X=0)\cdot 0^{2}=p\cdot 1^{2}+q\cdot 0^{2}=p=\operatorname {E} [X]}
From this follows
Var [ X ] = E [ X 2 ] − E [ X ] 2 = E [ X ] − E [ X ] 2 = p − p 2 = p ( 1 − p ) = p q {\displaystyle \operatorname {Var} [X]=\operatorname {E} [X^{2}]-\operatorname {E} [X]^{2}=\operatorname {E} [X]-\operatorname {E} [X]^{2}=p-p^{2}=p(1-p)=pq}[3]
With this result it is easy to prove that, for any Bernoulli distribution, its variance will have a value inside [ 0 , 1 / 4 ] {\displaystyle [0,1/4]}.
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