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Math Help - Random Variable PMF

  1. #1
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    Random Variable PMF

    A random variable X with PMF given by

    px(x) = {(x^2)/a, x=-3,-2,-1,0,1,2,3,
    0 otherwise}

    i believe a = 28 and E[X] = 0

    am i right in thinking this?

    What is the PMF of the random variable Y = (X-E[X])^2?

    Use the random variable Y to find Var[X]
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  2. #2
    MHF Contributor matheagle's Avatar
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    a=28 and moo is zero, I mean E(X), sry
    and the distribution of X is...

    P(X=-3)=P(X=3)=9/28

    P(X=-2)=P(X=2)=4/28=1/7

    P(X=-1)=P(X=1)=1/28

    NOW, let

    Y=X^2

    So, P(Y=9)=P(X=-3)+P(X=3)=18/28=9/14

    P(Y=4)=P(X=-2)+P(X=2)=2/7

    and P(Y=1)=P(X=-1)+P(X=1)=1/14

    E(Y)= 9(9/14)+4(2/7)+1(1/14), which better be the variance of X.
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    thank you! makes sense, i understand now!
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