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Mathematical axis problem of college entrance examination
Take the interval [0, a] on the number axis, and the coordinates of two points are random variables a, b,

Then a and b are independent of each other and obey the uniform distribution on [0, a].

The distribution function is f (x) = 0, x.

The distance between two points X=|A-B|=max(A, B)-min(A, b)

EX=Emax(A,B)-Emin(A,B)。

The distribution function of max(A, b) is g (x) = [f (x)] 2, from which Emax(A, B)=2a/3 can be obtained.

The distribution function H (x) of min(A, b) is 1-[ 1-f (x)] 2, from which Emin(A, B)=a/3 can be obtained.

EX=Emax(A,B)-Emin(A,B)=a/3。