$Y \sim N(\mu, \sigma^2)\implies (Y-\mu)/\sigma$
Prove that this has a Mean of $0$ and a Variance of $1$.
2026-03-27 00:55:06.1774572906
Beginner Econometrics question about probabilities for a normal variable
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If $X$ is a random variable, then $E(X + k) = E(X) + k,$ $E(cX) = c E(X),$ $Var(X + k) = Var(X),$ and $Var(cX) = c^2 Var(X).$ (These are facts for any random variable, including normal variables.)
If you already know these facts, you can use them to determine the mean and variance of $Y - \mu,$ then use them again to find your desired result.