Let $X$ have a normal distribution with mean $\mu$ and variance $\sigma^2$. Prove that $E(X-\mu)^2$=$\sigma^2$
2026-04-02 15:20:14.1775143214
Expectation formula proof
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The variance is defined by $$ \operatorname{Var}X=\operatorname E[X-\operatorname EX]^2. $$ $\operatorname EX=\mu$ for the normal distribution so you have that $\operatorname E[X-\mu]^2=\sigma^2$.