Q1 Let X and Y be independent exponential random variables with rates X and µ respectively where A> µ. Let c> 0. Q1(i.) Using conditioning arguments, show that the probability density function of X +Y...

Extracted text: Q1 Let X and Y be independent exponential random variables with rates X and µ respectively where A> µ. Let c> 0. Q1(i.) Using conditioning arguments, show that the probability density function of X +Y is given by fx+r (t): de -At -He H, t>0. ut Q1(ii.) Show that the conditional density of X, given that X +Y = c is (A – µ)e-(a-w)z fx|x+y (æ|c) = 0 < x="">< c.="" 1-e-(a-µ)c="" q1(ii.)="" use="" part="" (i)="" to="" find="" e[x|x="" +="" y="c]" q1(iv.)="" using="" the="" relationship="" c="E[X" +="" y|x+y="c]" =="" e[x[x="" +y="c]" +="" e[y\x="" +y="c]," deduce="" the="" value="" of="" e[y|x="" +y="">