Let X be a random variable with density function fX Show, using elementary calculus, that the function 1060 (a) E((X a)2) takes its minimum value when a (X), and in that case (a) 2(X)

Question: Let X be a random variable with density function fX. Show, using elementary calculus, that the function Ф(a) = E((X a)2) takes its minimum value

Let X be a random variable with density function fX. Show, using elementary calculus, that the function Ф(a) = E((X − a)2) takes its minimum value when a = μ(X), and in that case (a) = σ2(X).

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