f(y|x)=f(x,y)/f(x) = e^(-x)/(xe^(-x)) = 1/x, 0<y<x.
现在忙. 先做这些.追问
能不能写一下第（2）问的详细过程呢?
追答见图1. f(x)=∫[0,x] e^(-x)dy = xe^(-x), x>0.
f(y|x)=f(x,y)/f(x) = e^(-x)/(xe^(-x)) = 1/x, 0<y<x.
F(x) =∫[0,x] f(a) da =∫[0, x] ae^(-a)da = 1-[e^(-x)](1+x),
Fx(1) = 1-2e^(-1).
见图2. f(y) =∫f(x,y)dx =∫[y, ∞] e^(-x)dx = e^(-y), 0<y<∞.
F(y) =∫[0, y] f(a)da =∫[0, y] e^(-a)da = 1-e^(-y), y>0.
FY(1) = 1-e^(-1).
P(X≤1|Y≤1) = P(X≤1,Y≤1)/P(Y≤1) = P(X≤1)/P(Y≤1)
= {Fx(1)} / {FY(1)} = {1-2e^(-1)} / {1-e^(-1)} = (e-2)/(e-1) = 0.418
见图1. f(x)=∫[0,x] e^(-x)dy = xe^(-x), x>0.
f(y|x)=f(x,y)/f(x) = e^(-x)/(xe^(-x)) = 1/x, 0<y<x.
F(x) =∫[0,x] f(a) da =∫[0, x] ae^(-a)da = 1-[e^(-x)](1+x),
Fx(1) = 1-2e^(-1).
见图2. f(y) =∫f(x,y)dx =∫[y, ∞] e^(-x)dx = e^(-y), 0<y<∞.
F(y) =∫[0, y] f(a)da =∫[0, y] e^(-a)da = 1-e^(-y), y>0.
FY(1) = 1-e^(-1).
P(X≤1|Y≤1) = P(X≤1,Y≤1)/P(Y≤1) = P(X≤1)/P(Y≤1)
= {Fx(1)} / {FY(1)} = {1-2e^(-1)} / {1-e^(-1)} = (e-2)/(e-1) = 0.418
可以再写一下另一道题吗?
追答此图还是第一题的. 第二题不熟. 对不起. 请别人吧.