Question

The random variables X and Y have a joint probability denisty function fX,Y (x, y) = ce(ax2+bxy+dy2).

If a = −2, b = 4, d = −4, then determine
(a) c,
(b) E{X} and E{Y },
(c) rhoX,Y ,
(d) σ2 X and σ2 Y
(e) if X and Y are independent or not.

Answer 1

The joint probability density function is given by fX,Y (x, y) = ce(ax2+bxy+dy2). With specific values for a, b, and d, we can determine various properties of the random variables X and Y.

Step-by-step explanation:

a. c = 1/32

b. E{X} = 0 and E{Y} = 0

c. rhoX,Y = -1/4

d. σ^2X = 1/8 and σ^2Y = 1/4

e. X and Y are dependent