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Math Help - Proving that the Expected value of Z =0

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    Exclamation Proving that the Expected value of Z =0

    If Z = (X - MEAN) / Standard Deviation

    Prove that the expected value of Z = 0

    and that the variance of Z = 1
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    Hello,
    Quote Originally Posted by mibamars View Post
    If Z = (X - MEAN) / Standard Deviation

    Prove that the expected value of Z = 0

    and that the variance of Z = 1
    Let E(X)=m and Var(X)=\sigma^2=v
    You want to prove that Z=\frac{X-m}{\sigma} has an expected value of 0 and a variance of 1.


    Use these properties :
    (a is a constant)
    E(aX)=aE(X) (1)
    E(X+a)=E(X)+a (2)
    Var(aX)=a^2Var(X) (3)
    Var(X+a)=Var(X) (4)


    E(Z)=E \left(\tfrac{X-m}{\sigma}\right)=\frac{1}{\sigma} E(X-m)=\frac{1}{\sigma} [E(X)-m]
    But since E(X)=m, we can conclude that E(Z)=0.

    Now try to do it with the variance. It's easy with the formulae I gave above !
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