Using markov inequality, Let X be a random variable, not

Using markov inequality

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Reference no: EM131107185

Let X be a random variable, not necessarily positive.

(a) Using Markov's inequality, show that for x > 0 and t > 0,

assuming that E[e^tx]exists, where m is the mgf of X.

(b) For the case when X has a standard normal distribution, give the upper bound in Equation 9.5. Note that the bound holds for all t > 0.

The upper bounds in Equations 9.5 and 9.6 are called Chern off bounds.

Reference no: EM131107185

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