Let X and Y have the joint probability density function fx,y(x, y) = 1/x , x > 1, 0 < y < 1/x , zero elsewhere. a) Let U = XY . Find the p.d.f. of U, fu (u). Sketch the support. b) Let V = Y/X. Find the p.d.f. of V , fv (v). Sketch the support. c) Let U = Y and V = Y/X. Find the joint probability density function of (U, V ), fu,v (u, v). Sketch the support of (U, V ).

Let X and Y have the joint probability density function fx,y(x, y) = 1/x , x > 1, 0 < y < 1/x , zero elsewhere. a) Let U = XY . Find the p.d.f. of U, fu (u). Sketch the support. b) Let V = Y/X. Find the p.d.f. of V , fv (v). Sketch the support. c) Let U = Y and V = Y/X. Find the joint probability density function of (U, V ), fu,v (u, v). Sketch the support of (U, V ).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Let X and Y have the joint probability density function fx,y(x, y) = 1/x , x > 1, 0 < y < 1/x , zero elsewhere.

a) Let U = XY . Find the p.d.f. of U, fu (u). Sketch the support.

b) Let V = Y/X. Find the p.d.f. of V , fv (v). Sketch the support.

c) Let U = Y and V = Y/X. Find the joint probability density function of (U, V ), fu,v (u, v). Sketch the support of (U, V ).

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