Let the distribution function f (x) = a + bartanx of random variable x, and find P {x}
For the distribution function, f (x) = a + bartanx
F(-∞)=A+B(-π/2)=0
F(+∞)=A+B(π/2)=1
A=1/2,B=1/π
That is, f (x) = 1 / 2 + arctanx / π
F(1)-F(-1)=1/2+arctan(1)/π-(1/2+arctan(-1)/π)=1/2
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