Originally Posted by
mr fantastic (b) I suppose they want you to calculate the cdf of X: $\displaystyle F(x) = \int_0^x \lambda e^{-\lambda u} \, du$.
This should be a simple integral for you to calculate.
(c) Apply the definition: $\displaystyle M_X (t) = E\left(e^{tX}\right) = \int_0^{+ \infty} e^{tx} \lambda e^{-\lambda x} \, dx = \lambda \int_0^{+ \infty}e^{-(\lambda - t) x} \, dx $.
Again, this should be a simple integral for you to calculate. What happens if $\displaystyle \lambda - t < 0$ ....?