Pregunta: Let f(x,y)=2e−x−y for 0≤x≤y and x≤y<∞. Answer the questions below. You do not need to integrate by hand, you can use a computational tool To get full credit, show the set-up of the integral and then the answer. a. Check that the total probability is 1 . b. Find fx(x), the marginal pdf of X. c. Find fy(y) the marginal pdf of Y. d. Use b and c to check if X

Let $f(x,y)=2e^{-x-y}$ for $0\le x\le y$ and $x\le y<\infty$. Answer the questions below. You do not need to integrate by hand, you can use a computational tool To get full credit, show the set-up of the integral and then the answer. a. Check that the total probability is 1 . b. Find $f_x(x)$, the marginal pdf of $X$. c. Find $f_y(y)$ the marginal pdf of $Y$. d. Use $\mathrm{b}$ and $\mathrm{c}$ to check if $X$ and $Y$ are independent. Explain why or why not. e. Find $E(X)$, the mean of $X$. f. Find $E(Y)$, the mean of $Y$. g. Find $E(XY)$. Why is it not equal to $E(X)E(Y)$ ?