The question is shown below

Exercise 2 (3 + 1 + 3 + 3 pts.). Modeling. 1. Define 3 independent exponential variables . X the time until your friend Alex calls, with an average waiting time for his call 1/> (> > 0) . Y the time until your friend Jessica calls, with an average waiting time for her call 1/M (M > 0) . Z the time until your friend Mick calls, with an average waiting time for her call 1/v (v > 0) Let T be the time before any of those calls you. What is the cumulative distribution function of T? 2. In terms of the named distributions we have covered, what is the distribution of T? 3. Derive the p.m.f. of I defined by if X