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$(Y)=1$?
Obtaining a random var. with mean 0 and standard dev. 1
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probability
probability-theory
probability-distributions
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0Yes. This is the usual way of "standardizing" a random variable. – 2012-04-01
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0Unless $\sigma = 0$... – 2012-04-01