1. Let X-Poi(1) with =20. Hint: You may use EX=2, Var(X)=2, and Mx(t) = e^(-1) 1 a. Use a Chernoff bound to obtain an upper bound on p=Pr(X25). Find the sharpest (i.e., smallest) bound using this method. Give your answer using 3 decimal places. 1 b. Approximate p=Pr(X25) making use of the central limit theorem (CLT). Recall that if Y, -- Poi(u), i.i.d. i=1,...,n, then X="-Poi(^) with ==nu. Use this fact to write X = 20 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.)