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inequalities – Polynomial Markov versus Chernoff Bound for random variables

Suppose that $Xgeq0$, and that the significance producing duty of $X$ exists in an interval round 0. Given some $delta>0$ and integer $ok=1,2,…$, display that

$$inf_{ok=0,1,…}frac^ok){delta^ok} leq inf_{lambda>0} frac{E(e^{lambda X})}{e^{lambda delta}}. $$

Consequently, an optimized certain primarily based on polynomial moments is at all times not less than nearly as good

because the Chernoff higher certain. Could anybody enlighten me methods to show this?

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