a. Let X1, . . . , Xn be a random sample from a uniform distribution on [0, θ]. Then the...

a. Let X₁, . . . , X_n be a random sample from a uniform distribution on [0, θ]. Then the mle of is Y = max(X_i )Use the fact that Y ≤ y iff each Xi ≤ y to derive the cdf of Y. Then show that the pdf of Y = max(X_i ) is

b. Use the result of part (a) to show that the mle is biased but that (n + 1)max(X_i)/n is unbiased.