X - 1 1 2

P 0.3 0.4 0.3

e(x)=- 1×0.3+ 1×0.4+2×0.3 = 0.7

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:

The distribution law of discrete random variables and their distribution functions are unique to each other. They can all be used to describe the statistical regularity of discrete random variables, but the distribution law is more intuitive, concise and convenient to handle than the distribution function. Therefore, the distribution law (probability function) is generally used to describe discrete random variables instead of distribution function.

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