An experimental trial produces random variables x1nbspand, Basic Statistics

An experimental trial produces random variables x1nbspand

An experimental trial produces random variables X₁ and X₂ with correlation r = E[X₁X₂]. To estimate r, we perform n independent trials and form the estimate

Where X₁(i) and X₂(i) are samples of X₁ and X₂ on trial i. Show that if Var[X₁X₂] is finite, then ₁, ,... is an unbiased, consistent sequence of estimates of r

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