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I have calculated E(Y) for this problem and found it to be 0. However, I am now stuck on Var(Y). I seem to get stuck with either $E(Y^2)$ or $E(X^2)$ when solving it and I'm not sure how to solve those statements.

Let X be a random variable with expected value $\mu$ and variance $\sigma^2$. Let $Y = (X - \mu)/\sigma$. Compute E(Y) and Var(Y).

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Note that $$ EY^2=\frac{1}{\sigma^2}E[(X-\mu)^2]=\frac{1}{\sigma^2}\sigma^2=1 $$ by the (original) definition of variance whence $$ \text{Var}(Y)=EY^2-(EY)^2=1-0=1 $$

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  • $\begingroup$ What rule/how is the first part derived? $\endgroup$
    – user65909
    May 6, 2020 at 0:12
  • $\begingroup$ Nevermind, I understand now that its using the definition of variance. Thank you $\endgroup$
    – user65909
    May 6, 2020 at 2:16

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