Please answer the following question with steps, don't copy answers from other sources, thank you!

Problem 4 (20p). Let (X, ), , be an i.i.d. sequence of real-valued random variables with the expo- nential distribution with parameter o c (0, co). Show that (0.1) lim sup n-100 log (n) almost surely and (0.2) lim inf = 0 no log(n) almost surely