Question

3. Let the random variables X and Y have the joint probability density function fXY(x, y) = {1/y, 0 < y < 1, 0 < x < y 0, otherwise (a) Compute the joint expectation E(XY). (b) Compute the marginal expectations E(X) and E(Y). (c) Compute the covariance Cov(X, Y).

          3. Let the random variables X and Y have the joint probability density function
fXY(x, y) = {1/y, 0 < y < 1, 0 < x < y
             0, otherwise
(a) Compute the joint expectation E(XY).
(b) Compute the marginal expectations E(X) and E(Y).
(c) Compute the covariance Cov(X, Y).

3. Let the random variables X and Y have the joint probability density function
fXY(x, y) = 1/y, 0 < y < 1, 0 < x < y
0, otherwise
(a) Compute the joint expectation E(XY).
(b) Compute the marginal expectations E(X) and E(Y).
(c) Compute the covariance Cov(X, Y).

Added by Mary C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Kelan H

03/08/2022

Step 1

E(XY) = ∫∫ x*y*f(x,y) dx dy = ∫ from 0 to 1 ∫ from 0 to y 2xy dx dy = ∫ from 0 to 1 [x^2*y] from 0 to y dy = ∫ from 0 to 1 y^3 dy = [1/4*y^4] from 0 to 1 = 1/4. Show more…

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Let the random variables X and Y have the joint probability density function fxy(x, y) = {1/y, 0 < y < 1, 0 < x < y; 0, otherwise} (a) Compute the joint expectation E(XY). (b) Compute the marginal expectations E(X) and E(Y). (c) Compute the covariance Cov(X, Y).