Exercise 4 (3 + 1 + 3 + 3 points.). Modeling. 1. Define 3 independent exponential variables . X the time until your friend Alan calls, with an average waiting time for his call 1/) (> > 0) . Y the time until your friend Sara calls, with an average waiting time for her call 1// (A > 0) . Z the time until your friend Eli calls, with an average waiting time for her call 1/v (v > 0) Let T be the time before any of those three people call 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 0 if X