This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 powerlaw 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, ..., k1, 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....
View
Full
Document
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
 Chisholm
 Probability

Click to edit the document details