A nonnegative random variable X has moments which are known to be E [X] = 1 ,

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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,
A nonnegative random variable X has moments which are known

(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).

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