 Solution

ID: 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/solution

f_{X}

, its mean is

μ = E [X] = \int_{- \infty}^{\infty} x f_{X} (x) d x,

provided

\int_{- \infty}^{\infty} ∣ x ∣ f_{X} (x) d x < \infty

. Its variance is the expectation of the squared deviation from its mean:

var (X) = E [(X - μ)^{2}] = \int_{- \infty}^{\infty} (x - μ)^{2} f_{X} (x) d x .

This is finite when

E [X^{2}] < \infty

; otherwise it may be

+ \infty

if the finite mean exists.

 New to topics? Read the docs here!