Question 3Let X1,..., Xk, . .. be independent random variables having the common cumulativedistribution function F. For a fixed positive integer n, define Ynmax(X1,..., X,).Suppose N is a geometric random variable with parameter p and N is independent of{X;, i = 1,2, ...}. Define YNmax(X1,..., XN).(a) Find the cumulative distribution function of Yn.(b) If X; ~ U(0, 1), find E[Y„].(c) Find P(YN

Question 3 Let X1,..., Xk, . .. be independent random variables having the common cumulative distribution function F. For a fixed positive integer n, define Yn max(X1,..., X,). %3D Suppose N is a geometric random variable with parameter p and N is independent of {X;, i = 1, 2, ...}. Define YN max(X1,..., XN). (a) Find the cumulative distribution function of Yn. (b) If X; ~ U(0, 1), find E[Y,„].