Past exam of the mathematics course of the University of Oxford / 2015 / Prelims / Mathematics III / 6 / a / i

For a random variable with a continuous probability distribution and probability density function $f_X$, the mean and variance areA finite mean requires $\int |x|f_X(x)dx<\infty$. A finite variance additionally requires the second moment to be finite; without that condition the nonnegative integral for the variance may be infinite.