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Let $(\Omega,\mathcal F,\mathbf P)$ be a probability space. Suppose a random variable $X$ has expectation $\mu=\mathbf E(X)$ and variance $\sigma^2=\mathrm{Var}(X)$. Does the random variable $Y$ given by $Y=\frac{X-\mu}\sigma$ satisfy $\mathbf E(Y)=0$ and Var$(Y)=1$?

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    Yes. This is the usual way of "standardizing" a random variable.2012-04-01
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    Unless $\sigma = 0$...2012-04-01

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