STAT 410 Examples for 09/24/2008 Fall 2008 1. Let X and Y be two independent Exponential random variables with mean 1. Find the probability distribution of Z = X + Y. That is, find ( ) z f Z = ( ) z f Y X + . 2. Let X and Y be two independent Exponential random variables with mean 1. Find the p.d.f. of Z = 2 X + Y. Fact : Let X and Y be independent continuous random variables. Then ( ) ( ) ( ) ∞ ∞-=-+ ⋅ dx x w f x f w f Y X Y X . (convolution) 3. Let X 1 and X 2 be be two independent χ 2 random variables with m and n degrees of freedom, respectively. Find the probability distribution of W = X
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Probability distribution, Probability theory, probability density function