L13_S10 - AMS 311, Fall Semester, 2010 Chapter Six Jointly...

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Unformatted text preview: AMS 311, Fall Semester, 2010 Chapter Six Jointly Distributed Random Variables 6.3. Sums of Independent Random Variables In a gambling problem, let X be the winnings from one play of a game of chance and have pdf X f , and Y be the winnings from one play of another game of chance with pdf Y f , with X and Y independent. The random variable Y X S + = represents the total winnings from the two games. Then - +- = + = = . ) ( ) ( } { ) ( ) ( dy y f y s F s Y X P s F s F Y X Y X S Further, . ) ( ) ( ) ( dy y f y s f s f Y X Y X - +- = Example 3a. Sum of two independent uniform random variables . If X and Y are two independent random variables, both uniformly distributed on (0,1) calculate the probability density of . Y X S + = Proposition 3.1. If X and Y are independent gamma random variables with respective parameters ) , ( s and ), , ( t then Y X S + = is a gamma distribution with parameters ). , ( t s + If n i X i , , 1 , = are independent gamma random variables with respective parameters...
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This note was uploaded on 04/13/2010 for the course AMS 311 taught by Professor Tucker,a during the Spring '08 term at SUNY Stony Brook.

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L13_S10 - AMS 311, Fall Semester, 2010 Chapter Six Jointly...

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