if X is an exponential random variable with mean 1/lambda, show that the expected value of x^k = k!/lambda^k

Hint: make use of the gamma density function

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- Oct 29th 2010, 06:18 AMholly123hard proof- gamma distribution
if X is an exponential random variable with mean 1/lambda, show that the expected value of x^k = k!/lambda^k

Hint: make use of the gamma density function - Oct 29th 2010, 06:53 AMTheEmptySet
The density function for an exponential is

so

let and the resulting integral is the gamma function.

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