Question

已知连续型随机变量的分布函数如下（如图），求A、B、概率密度f（x）、P{1<X<2}

如图

Answer 1

(1)
F(x)
=Ae^x ; x<0
=B-Ae^(-x) ; x≥0
lim(x->+∞) F(x) = 1
lim(x->+∞) [ B-Ae^(-x) ] = 1
B=1
F(0+)=F(0) = B-A
F(0-)= A
F(0+)=F(0-)
B-A =A
A= B/2 = 1/2
ie
(A,B)= (1/2, 1)
(2)
f(x)
=F'(x)
=(1/2)e^x ; x<0
=(1/2)e^(-x) ; x≥0
(3)
P(1<X<2)

=∫(1->2) (1/2)e^(-x) dx
=-(1/2)[ e^(-x) ](1->2)
=(1/2) [ e^(-1) - e^(-2) ]

Answer 2

清福神 ? 三界首领八部三百六十五位清福正神 柏鉴