Consider a random variable X following the exponential distribution X-f(x), where f(x) = aeax for x > 0 and 0 otherwise, a > 0. Derive its moment-generating function Mx(t) and specify its domain (where it is defined or for what t does the integral exist). Use it to compute the first four non-central moments of X and then derive the general formula for the nth non-central moment for any positive integer n. Also, write down the expression for variance, skewness, and kurtosis.