Show that if X has a mgf bounded by the mgf of exponential distribution (i.e., /( t) for t 1 we have P{X> }

Show that if X has a mgf bounded by the mgf of exponential distribution (i.e., λ/(λ −

t) for t<λ), then for λ

> 1 we have P{X>

} ≤ λ

e−(λ−1).

(Hint: Use the mgf of exponential distribution to obtain the bound for P{X>

}, then determine its minimum.)