Let X and Y be independent and N(0, 1) distributed random variables. Let U = X and V = X/Y. Show that the random variable V is Cauchy distributed and find E(V ). **Problem Statement:**Let $ X $ and $ Y $ be independent and $ N(0, 1) $ distributed random variables. Let $ U = X $ and $ V = \frac{X}{Y} $. Show that the random variable $ V $ is Cauchy distributed and find $ E(V) $.

Since X~N(0,σ2), X~N(0,σ2), then we havedF(x,y)=f1(x)f2(y)dxdy=(1σ2π)2exp[-12σ2(x2+y2)]dxdyLet xy=u,…

Answered: Let X and Y be independent and N(0, 1)…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Let X and Y be independent and N(0, 1) distributed random variables. Let U = X and V = X/Y. Show that the random variable V is Cauchy distributed and find E(V ).

**Problem Statement:**

Let $ X $ and $ Y $ be independent and $ N(0, 1) $ distributed random variables. Let $ U = X $ and $ V = \frac{X}{Y} $. Show that the random variable $ V $ is Cauchy distributed and find $ E(V) $.

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