Expectation of uniform distribution: The expectation of uniform distribution is the midpoint (a+b)/2 of the value interval [a, b]. ?

Variance of uniform distribution: var(x)=E[X? ]-(E[X])？

var(x)=E[X？ ]-(E[X])？ = 1/3(a？ +ab+ b？ )- 1/4(a+b)？ = 1/ 12(a？ -2ab+ b？ )= 1/ 12(a-b)？

If x obeys uniform distribution on [2,4], then the mathematical expectation ex = (2+4)/2 = 3; Variance DX=(4-2)? / 12= 1/3。

Extended data

1, standard uniform distribution

If a = 0 and b = 1, the obtained distribution U(0, 1) is called standard uniform distribution.

An interesting property of standard uniform distribution is that if u 1 has a standard uniform distribution, then 1-u 1 also has it. ?

2. Correlation distribution

(1) If x obeys the standard uniform distribution, then Y = Xn has a parametric β distribution (1/n, 1).

(2) If x obeys the standard uniform distribution, then Y = X is also a special case of β distribution with parameters (1, 1).

(3) The sum of two independent uniform distributions produces a symmetrical triangular distribution.

Baidu Encyclopedia-Uniform Distribution