Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Discrete mathematics, continuous mathematics and probability (resit) / 9 / a / ii

For an absolutely continuous probability distribution, its expectation isThis is finite when ${\int }_{-\infty }^{\infty }|x|f_X(x)dx<\infty$. More generally it is an extended real value if only one of the positive and negative parts diverges; it is undefined if both diverge. For nonnegative $X$ it always exists in $[0,\infty ]$.