Full details (including description of methods used and explanation, key formula and theorem used and final answer) are required.

Use Markov's inequality to show that, for any t > 0 and any random variable such that E(etx ) exists, P(X > a) S e-at E(etx) for a > 0. Such that P(X > a) S infle-at E(etx) }. Hence show that if X is Poisson with parameter 1, and x > 1, X P(X 2 x) S ex-1