Question

设随机变量X,Y相互独立,其概率密度函数分别为 fx(x)=1 0

Answer 1

设T=2X-Y

X=(Z+T)/4

Y=(Z-T)/2

|det(jcobian)|=|-1/8-1/8|=1/4

f(x(z,t),y(z,t))=e^(-y)=e^(-(z-t)/2)=e^((t-z)/2)

f(z,t)=(1/4)e^((t-z)/2)

t=2x-y, -无穷