Let \(X\) be a random variable with \(\mathbf{E}(X)=\mu\) and \(\mathbf{Var}(X)=\sigma^2\). Show that for any constant \(a\)
\[\mathbf{E}\big[(X-a)^2\big]=\sigma^2+(\mu-a)^2\]
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Let \(X\) be a random variable with \(\mathbf{E}(X)=\mu\) and \(\mathbf{Var}(X)=\sigma^2\). Show that for any constant \(a\)
\[\mathbf{E}\big[(X-a)^2\big]=\sigma^2+(\mu-a)^2\]