Show the mean equals the standard deviation of the exponential random variable function.
Here's a kick start
For $\displaystyle \displaystyle f(x) = \lambda e^{-\lambda x}$
Find
$\displaystyle \displaystyle E(x) = \int_0^\infty x\times f(x)~dx$
$\displaystyle \displaystyle SD(x) =\sqrt{Var(x)} = \sqrt{\int_0^\infty(x-E(x))^2\times f(x)~dx}$