 # inequalities – Polynomial Markov versus Chernoff Bound for random variables Answer

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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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