Mathematical expectation e(x) describes the "average" or "expected" value of random variable X. For discrete random variables, mathematical expectation is defined as: e(x) equals ∑kxkpk. Where xk is all possible values of the random variable x and pk is the probability that x takes xk. For continuous random variables, mathematical expectation is defined as: e(x) equals ∫? ∞∞xf(x)dx .

Where f(x) is the probability density function of random variable x.

Variance d(x) describes the deviation degree of random variable X from its mathematical expectation e(x). Variance is defined as: d(x) equals e[(x minus e(x))2]. For discrete random variables, the variance can be expressed as: d(x) equals Σ k (xk minus e(x))2pk. For continuous random variables, the variance can be expressed as: d(x) equals ∫? ∞∞∞ x minus e(x)) 2f(x)dx.