Question

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

Answer 1

Answer:

Please find the complete question in the attached file.

Step-by-step 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:

$\to f(x_2|x_1)=\frac{f(x_1,x_2)}{f(x_1)}\ =\frac{e^{-x_1}}{x_1\ e^{-x_1}}=\frac{1}{x_1} ; \\\\ \ \ 0\leq x_2 \leq x_1$

For point c:

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