当y≤0时,F(y)=P(Y
当y>0时, F(y)=P(Y-√y)=P(X<√y)+1-P(X≤-√y)
f(y)=F'(y)=[1/π(1+y)][1/(2√y)]-[1/π(1+y)][-1/(2√y)]=1/π(1+y)][1/√y]
2. E(arctanX)=∫(-∞,+∞)arctanX[1/π(1+x^2)]dx=(1/2π)(arctanX)^2︱(-∞,+∞)
=2(1/2π)(π/2)^2=π/4