Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Discrete mathematics, continuous mathematics, and probability / 9 / a / i

For a continuous random variable with probability density function $f_X$, its mean isprovided ${\int }_{-\infty }^{\infty }|x|f_X(x)dx<\infty$. Its variance is the expectation of the squared deviation from its mean:This is finite when $\mathbb{E}[X^2]<\infty$; otherwise it may be $+\infty$ if the finite mean exists.