Introduction to Probability · Problem 9.3.1

Generating Functions — Grinstead & Snell

Mathematics — Probability · central-limit-theorem-continuous

Problem

Let XX be a continuous random variable with mean μ(X)\mu(X) and variance σ2(X)\sigma^2(X), and let X∗=(X−μ)/σX^* = (X - \mu)/\sigma be its standardized version. Verify directly that μ(X∗)=0\mu(X^*) = 0 and σ2(X∗)=1\sigma^2(X^*) = 1.

Related theory

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