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Math Help - prove or disprove Variance = p(1-p) for bernoulli mass function

  1. #1
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    prove or disprove Variance = p(1-p) for bernoulli mass function

    given Ber(x,p) = Pr(X=x) = {p , x=1
    {1-p , x=0
    { o , else

    Let p e(0,1) and X~Ber(x,p). Prove or disprove that Var[x]= p(1-p).

    no idea where to start on this one guys...
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  2. #2
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    Quote Originally Posted by nikie1o2 View Post
    given Ber(x,p) = Pr(X=x) = {p , x=1
    {1-p , x=0
    { o , else

    Let p e(0,1) and X~Ber(x,p). Prove or disprove that Var[x]= p(1-p).

    no idea where to start on this one guys...
    Start with the definition of variance:

    \text{Var}(x)=E((x-\overline{x})^2)

    We have \text{Pr}(X=1)=p,\ \text{Pr}(X=0)=1-p and all other values have probability zero.

    So:

    \overline{x}=E(x)=(1\times p) + (0 \times (1-p))=p

    and:

    E((x-\overline{x})^2)=(1-p)^2 \times p+(0-p)^2\times (1-p)=..

    CB
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