18. If X is an exponential random variable with mean 1/, show that $$E[X^k] = frac{k!}{lambda^k}$$ k

18. If X is an exponential random variable with mean 1/λ, show that

$$E[X^k] = \frac{k!}{\lambda^k}$$ k = 1, 2,...

HINT: Make use of the gamma density function to evaluate the above.