Question

概率论，第5题，求解

Answer 1

令P2 = P{2<X<3}， P1 = P{1<X<2}
P2/P1 = ∫(2,3) φ(x)dx / ∫(1,2) φ(x)dx = 2

∫(Ax+B)dx = Ax^2/2 + Bx + C
令 F(x) = Ax^2/2 + Bx
F(3) - F(2) = 2 ((F(2) - F(1))
F(3) = 3 F(2) - 2F(1)
9A/2 + 3B = 6A + 6B - A - 2B
A = -2B .... (1)

P{-∞<X<∞} = ∫(-∞,∞) φ(x)dx = ∫(1, 3) φ(x)dx
1 = F(3) - F(1)
1 = 4A + 2B ....(2)

(1), (2) 联立，解得 A = 1/3, B = -1/6