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Statistics MLE homework

Overview

2 Questions - one of them is attached

1. Suppose that X1, · · · , Xn are iid with pdf f(x|θ) = 2x/(θ^2), 0 < x ≤ θ, zero elsewhere. (a) Show that the maximum likelihood estimate (MLE) of θ is X(n) = max(X1, · · · , Xn) and obtain pdf of X(n). (b) Find the MLE for the median of Xi .