Question

Let X1 and X2 have the joint pdf, f(x1, x2) 0

Answer 1

Please find the complete question in the attached file.

Explanation:

For point a:

`\to fx_1(x_1)=\int^{x_(1)}_(0) f(x_1,x_2)\ dx\\\\`

`=\int^{x_(1)}_(0) e^(-x_1)\ dx_2\\\\= e^(-x_1) \ [x_2]^(x_1)_0 \\\\\therefore f x_1(x_1)=x_1e^(-x_1); \ \ x_1>0\\\\`

For point b:

`\to f(x_2|x_1)=(f(x_1,x_2))/(f(x_1))\ =(e^(-x_1))/(x_1\ e^(-x_1))=(1)/(x_1) ; \\\\ \ \ 0\leq x_2 \leq x_1 \\\\`

For point c:

`P(x_1>2|x_2=7)= 1.00 \\\\\because x_2=7\to x_1>7\to x_1>2\\\\`