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Unformatted text preview: STAT 333 - Spring 2009 - Assignment 2 Due: Thursday, June 18 at 2:30 pm (in class) Type I Problems 1. Suppose X has probability density function f ( x ) = 2 x- 3 for x 1. (This is called a power-law or Pareto distribution.) Suppose Y is independent of X and has a gamma distribution with parameters = 4 and = 2. Obtain P ( X > Y ). 2. #37, page 171 of the text, 9th edition. 3. #44, page 173 of the text, 9th edition. 4. #62, page 176 of the text, 9th edition. Type II Problems 1. For each of the following distributions, find the pgf G X ( s ), find the radius of conver- gence, and use it to find E [ X ] and Var( X ). (a) X is a Poisson random variable with parameter . (b) X is a discrete uniform random variable over the integers 1, 2, ..., k-1, k . That is, P ( X = i ) = 1 /k for each of i = 1, ..., k . 2. Suppose we toss a fair coin repeatedly and observe a sequence of H or T. Let be the event T T H H....
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This note was uploaded on 01/16/2011 for the course STAT 333 taught by Professor Chisholm during the Spring '08 term at Waterloo.
- Spring '08