Q1 Let X and Y be independent exponential random variables with rates A and u respectivelywhere X > u. Let c > 0.Q1(i.) Using conditioning arguments, show that the probability density function of X+Y isgiven byfx+y(t) =detutHet > 0.Q1(ii.) Show that the conditional density of X, given that X+ Y = c is(1 – 4)e-(d-w)x1- e-(A-u)cfx\X+Y (x|c)0 < x < c.Q1(iii.) Use part (i) to find E[X|X +Y = c]Q1(iv.) Using the relationshipc = E[X +Y|X +Y = c] = E[X[X +Y = c] + E[Y|X +Y = c], deduce the value ofE[Y|X+Y = c].

Answered: Q1 Let X and Y be independent…

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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