a) For a whole numbered, non-negative random variable, show that it is true that:

E(X) = Sum(n=1 to infinity) of P(X>=n)

b)Let X be a non-negative continuously distributed random variable with probability density f and distribution function F. Show that:

E(X) = Integral(0 to infinity) of (1-F(X))dx

c) Here's the one that I can't get.

Formulate and prove an appropriate formula for E(X^n), n is a natural number. Use this formula to find the expected value of the Exponential Distribution with Parameter lambda.

I can get the second part of this question, but I need some help getting started by finding the formula for E(X^n). I'm not sure where to start. I know that the expected value of the Exponential Distribution is simply lambda. Any hints? Thanks.