Question: A nonnegative random variable X has moments which are known to be E [X] = 1 , E [X2] = 2 , E [X3] =

A nonnegative random variable X has moments which are known to be E [X] = 1 , E [X2] = 2 , E [X3] = 5 , E [X4] = 9 , E [X5] = 14 , E [X6] = 33. (a) Show that for any nonnegative random variable,
(a) Show that for any nonnegative random variable,

(b) Using the result of part (a) and the values of the moments given, find the tightest bound on Pr (X ‰¥2).
(c) Using the result of part (a) and the values of the moments given, find the tightest bound on Pr (X ‰¥ 3).

Pr(X210) . 0

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