Question: 6.4 Suppose that X admits a moment generating function MX. Prove that P(X x) etxMX(t) for every t > 0 and P(X

6.4 Suppose that X admits a moment generating function MX. Prove that P(X ≥ x) ≤ e−txMX(t) for every t > 0 and P(X ≤ x) ≤ e−txMX(t) for every t < 0.

These are known as the Chernoff bounds on the probability.

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