Question

Let (X,Y) have a joint pdf given by f(x,y) = { 1; if |y| < x; 0 < x < 1, 0, otherwise. a) Find the marginal pdf for X and Y respectively. b) Find the conditional densities fX|Y and fY|X. c) Find the Cov(X,Y).

          Let (X,Y) have a joint pdf given by

f(x,y) = {
1; if |y| < x; 0 < x < 1,
0, otherwise.

a) Find the marginal pdf for X and Y respectively.
b) Find the conditional densities fX|Y and fY|X.
c) Find the Cov(X,Y).

Added by Miguel W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

06/19/2023

Step 1

For X: $$ f_X(x) = \int_{-x}^{x} f(x,y) dy = \int_{-x}^{x} 1 dy = [y]_{-x}^{x} = x - (-x) = 2x $$ So, the marginal pdf for X is: $$ f_X(x) = \begin{cases} 2x, & 0 < x < 1 \\ 0, & \text{otherwise} \end{cases} $$ For Y: $$ f_Y(y) = \int_{|y|}^{1} f(x,y) dx = Show more…

Show all steps

Thanks for your feedback!

Let (X,Y) have a joint pdf given by f(x,y) = { 1; if |y| < x; 0 < x < 1, 0, otherwise. a) Find the marginal pdf for X and Y respectively. b) Find the conditional densities fX|Y and fY|X. c) Find the Cov(X,Y).