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Unformatted text preview: STAT 410 Fall 2008 Homework #1 (due Friday, September 5, by 3:00 p.m.) 1. Consider a continuous random variable X with probability density function f X ( x ) = & & < < o.w. 1 3 2 x x Find the moment-generating function of X, M X ( t ). 2. Suppose a discrete random variable X has the following probability distribution: P( X = k ) = ( ) ! 2 ln k k , k = 1, 2, 3, . a) Verify that this is a valid probability distribution. b) Find X = E ( X ) by finding the sum of the infinite series. c) Find the moment-generating function of X, M X ( t ). d) Use M X ( t ) to find X = E ( X ). 3. Suppose a random variable X has the following probability density function: & & =-otherwise 1 ) ( x C x f x e a) What must the value of C be so that f ( x ) is a probability density function? b) Find the cumulative distribution function F ( x ) = P( X x )....
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This note was uploaded on 10/22/2009 for the course STAT 410 taught by Professor Alexeistepanov during the Fall '08 term at University of Illinois at Urbana–Champaign.
- Fall '08