Let X1,X2,... be independent random variables. Fix p in the interval (0,1), and for n1 let Xn have the geometric (pn) distribution on {1,2,3,...}.

In what follows, remember that if you have infinite sums in your answers, then you must simplify them.

a) For k1, write P(X1>k) in terms of p and k.

b) Find P(X1>X2).

c) Find an exponential approximation to P(Xn>n) for large n.