Consider two independent random variables X1 andX2 having the same Cauchy distributionf(x) = 1π(1 + x2)for − q < x < qFind the probability density of Y1 = X1 + X2 by usingTheorem 1 to determine the joint probability density ofX1 and Y1 and then integrating out x1. Also, identify thedistribution of Y1.

Consider two independent random variables X1 andX2 having the same Cauchy distributionf(x) = 1π(1 + x2)for − q < x < qFind the probability density of Y1 = X1 + X2 by usingTheorem 1 to determine the joint probability density ofX1 and Y1 and then integrating out x1. Also, identify thedistribution of Y1.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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