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Unformatted text preview: = 1 . Prove that f is a density of some random variable X . (Construct X ). 5. (15 pts) Let A be a point chosen uniformly at random from the circle x 2 + y 2 = 1. Compute the expectation of the distance from A to some xed line through the origin. 6. Let X be a non-negative random variable such that E X exists. (a) (10 pts) Show by example that E ( X 2 ) may not exist. (b) (15 pts) Consider the truncation X n = min( X, n ). Prove that for every p > 2, s n =1 n-p E ( X 2 n ) < . (c) (15 pts: bonus problem) . Prove this for p = 2....
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This note was uploaded on 01/25/2011 for the course STAT 235a at Stanford.