Let X 1 , ,X n be a random sample from a distribution of the continuous type with cdf F(x) Let P(X 1 a) F(a), where a is known Show that the proportion n 1 X i a is the MVUE of

Question: Let X 1 , . . .,X n be a random sample from a distribution of the continuous type with cdf F(x). Let =

Let X₁, . . .,X_n be a random sample from a distribution of the continuous type with cdf F(x). Let θ = P(X₁ ≤ a) = F(a), where a is known. Show that the proportion n⁻¹#{X_i ≤ a} is the MVUE of θ.

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