5. Suppose X and Y are two independent Uniform(0, 1) random variables. Use the cumulative distribution function method to find the probability density function of their sum U = X+Y. Solution: Given that X = (0,1) and Y = (0, 1), we have U € (0,2). Then for u € (0,2), the equality U = u implies that X = u-Y. Hence, since we want 0 Uu, we observe that we need 0≤x≤u-Y, which is possible if and only if Y
5. Suppose X and Y are two independent Uniform(0, 1) random variables. Use the cumulative distribution function method to find the probability density function of their sum U = X+Y. Solution: Given that X = (0,1) and Y = (0, 1), we have U € (0,2). Then for u € (0,2), the equality U = u implies that X = u-Y. Hence, since we want 0 Uu, we observe that we need 0≤x≤u-Y, which is possible if and only if Y
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 22E
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Could you explain how the inequalities u in (0,1), we have 0 ≤ X ≤u-Y for any 0 ≤Y<u and u in (1,2), we either have 0 ≤ X ≤u-Y for any u - 1 < Y<1, or 0≤x≤1 for any 0 ≤Y≤u - 1 are obtained please. They're in the solutions but don't understand how they were derived.
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