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Assignment2

# Assignment2 - STAT 333 Spring 2009 Assignment 2 Due...

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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 α = 4 and λ = 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 λ . (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 λ be the event ”T T H H”. (a) Why is λ a renewal event? (b) Use the renewal sequence r n to show that λ is recurrent.

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Assignment2 - STAT 333 Spring 2009 Assignment 2 Due...

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