Page 128 - Schaum's Outlines - Probability, Random Variables And Random Processes

CHAP. 3) MULTIPLE RANDOM VARIABLES

Ans. 1 - e-"2/(2@2)

3.67. Let (X, Y) be a bivariate normal r.v., where X and Y each have zero mean and variance a2, an( f the
correlation coefficient of X and Y is p. Find the joint pdf of (X, Y).

3.68. The joint pdf of a bivariate r.v. (X, Y) is given by

(a) Find the means and variances of X and Y.
(b) Find the correlation coefficient of X and Y.
Ans. (a) p, = p, = 0 ax2 = aY2 = 1
(b) P = 3

3.69. Let (X, Y, 2) be a trivariate r.v., where X, Y, and Z are independent and each has a uniform distribution
over (0, 1). Compute P(X 2 Y 2 Z).
Ans. 3