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 nonnegative 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 np E ( X 2 n ) < ∞ . (c) (15 pts: bonus problem) . Prove this for p = 2....
View
Full Document
 '07
 RomanVershynin
 Probability, Variance, ex, 10 pts, 20 pts, 15 pts

Click to edit the document details