The expectation of discrete random variables, that is, the average value of discrete random variables, represents the middle level of a random variable, and the variance of random variables describes the discrete degree of random variables.

Because they reflect the average level and stability of random variables, the mean and variance of random variables have important applications in market forecasting.

Expected formula of discrete random variables: the probability that the value of discrete random variable X is X 1, X2, X3...Xn, p(X 1), p(X2), P (X3)...P (Xn) is the corresponding value of X can be understood as data X 1, X2.

Then e (x) = x1* p (x1)+x2 * * p (x2)+...+xn * * p (xn) = x1* f1(x/kloc-0

Variance formula of discrete random variables: d (x) = e {[x-e (x)] 2} = e (x 2)-(ex) 2.

Variance and expectation of normal distribution;

1, uniform distribution: the expected value is (a+b)/2, and the variance is the square of (b-a)/12.

2. Binomial distribution: the expectation is np and the variance is npq.

3. Poisson distribution: the expectation is p and the variance is p.

4. Exponential distribution: the expected value is 1/p, and the variance is1/(the square of p).

5. Normal distribution: expectation is U, variance is&; The square of.

6. If X obeys the 0- 1 distribution with the parameter p, then E(X)=p and d(X)=p( 1-p).