Let x1; x2; be i. i.d. expo(1). (a) let n = min : xn be the index of the xj to exceed 1. find the distribution of (give the name and parameters), and hence nd e(n). (b) let m = min: x1 + x2 + + xn be the number of xj's we observe until their sum exceeds 10 for the rst time. find the distribution of (give the name and parameters), and hence nd e(m). hint: consider a poisson process. (c) let x n = (x1 + + xn)=n. find the exact distribution of x n (give the name and parameters), as well as the approximate distribution of x n for n large (give the name and parameters).