Let X_1, X_2, ... be independent, U(0, 1)-distributed random variables, and let Nm be Po(m)-distributed variable independent of X_1, X_2, .... Let Vm = max{X_1, X_2,..., X_Nm}.
(a) Determine the distribution of Vm.
(b) Determine the moment generating function of Vm.
(c) Show that Vm converges to 1 in probability.
(d) Show that m*( (Vm) - 1) converges in distribution as m->infinity and determine the limit distribution.