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Let X ~Pois() and > 0. (a) Show that P[X (1 + )] e [(1+) log(1+)]. Hint: first show that P[X (1 + )] inft

Let X ~Pois() and > 0.

(a) Show that P[X (1 + )] e[(1+) log(1+)].

Hint: first show that P[X (1 + )] inft>0 e(1+)tMX(t) and then optimize over t.

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