How do we use the inequality and the central limit theorem to answer the questions?

Suppose X1, . . .. X\" we Exponential] are independent random variables each drawn from the common unit exponential distribution. In our usual notation, let Sn = X1 + - - - + X.\" . Fix any 3 3.3- 0. Your task is to estimate the tail probability Pl}; 2 n. + t}. {a} Use Cherno's inequality to nd an upper bound for the tail probability. {b} Use the central limit theorem to obtain a hopeful asymptotic approximation for the tail probability. {c} Comment on howl;r your two estimates compare when t = 11 for some tiny E L} {1 'Which approximation do you think is better? [Hints: For {a} recall that P{Sn 2 n + t} i minty-Eu. E (EC{S\"_\"_). For the comparison segment for {b} recall that 1:5 (at) do: 5 is'EJ