1. Let X - Poi(1) with 1 =20. Hint: You may use EX = 1, Var(X) =1, and My(t) = elle'-1) 1 a. Use a Chernoff bound to obtain an upper bound on p =Pr(X 2 25) - Find the sharpest (i.e., smallest) bound using this method. Give your answer using 3 decimal places. 1 b. Approximate p=Pr(X 2 25) making use of the central limit theorem (CLT). Recall that if Y, ~ Poi(#), iid. i=1, ...,n, then X" = > Y - Poi(A) with A = _ u=nu. Use this fact to write X" = > Y , with Y - Poi(1) and then use the CLT to approximate p. Compute any z-score with at least 6 decimal places. Give your answer using 3 decimal places. Do *not* use a "continuity correction." (The answer computed with a continuity correction will not be counted correct.)