a Let X1, , Xn be a random sample from a uniform distribution on 0, Icirc cedil Then the mle of u is Icirc cedil Y max(Xi) Use the fact that Y curren y iff each Xi curren y to derive the cdf of Y Then show that the pdf of Y max(Xi) is b Use the result of part (a) to show that the mle is biased but that (n 1)max(Xi)Yn is unbiased ny 1 0 otherwise

Question: a. Let X1,... , Xn be a random sample from a uniform distribution on [0, Î¸]. Then the mle of u is Î¸^ = Y

a. Let X1,... , Xn be a random sample from a uniform on [0, Î¸]. Then the mle of u is Î¸^ = Y = max(Xi). Use the fact that Y ‰¤ y iff each Xi ‰¤ y to derive the cdf of Y. Then show that the pdf of Y = max(Xi) is

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

ny-1 0 otherwise

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