易知z0)
Fz(z)=∫[0->+∞]dx∫[0->z/x] xe^(-x(1+y))dy
=∫[0->+∞]xe^(-x) - xe^(-(z+x)) dx
=-xe^(-x) | [0->+∞] - ∫[0->+∞]-e^(-x)dx - [(-xe^(-(z+x))) | [0->+∞] + ∫[0->+∞]e^(-(z+x))dx]
=0+1-[0+e^(-z)]
=1-e^(-z)
0,z0
0,z0
易知z0)
Fz(z)=∫[0->+∞]dx∫[0->z/x] xe^(-x(1+y))dy
=∫[0->+∞]xe^(-x) - xe^(-(z+x)) dx
=-xe^(-x) | [0->+∞] - ∫[0->+∞]-e^(-x)dx - [(-xe^(-(z+x))) | [0->+∞] + ∫[0->+∞]e^(-(z+x))dx]
=0+1-[0+e^(-z)]
=1-e^(-z)
0,z0
0,z0