Let (X)=2 be an i.i.d. sequence of real-valued random variables with the exponential distribution with parameter a € (0,0). Show that 1 (0.1) lim sup X n7" log(n) almost surely and (0.2) X lim inf 11+ log(n) 0 almost surely. Note: The above are the limit superior/inferior of sequences of real numbers, not of events. Hint: Look to the proof of the Strong Law of Large Numbers in Lecture 24 for inspiration.