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Unformatted text preview: X,Z ). (c) Find Var[ Z | Y ]. Problem 4. Suppose X has pdf f X ( x ) = ( x -1 if 0 < x < 1 , otherwise . Here, > 0. (a) Find the cdf F X of X . (b) Find EX . (c) Find the likelihood function f x 1 ,...,x n | for this distribution given a random sample x 1 ,...,x n . (d) Find the maximum likelihood estimator MLE of . Problem 5. Suppose X 1 ,...,X n are iid and have a distribution depending upon a parameter R . Suppose n is an estimator for (based on a sample of size n ) whose pdf is given by f ( t ) = n 2 e- n | t- | . Suppose 0 < < 1. Find a such that [ -a, + a ] is a (1- )-level condence interval for ....
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- Fall '07