Jeonsah

04-22-2012, 06:12 PM

I need some help with the following problem:

Random variables X and Y are jointly distributed with a bivariate Gaussian (Normal) distribution with E[X]=3, E[Y]=2, pxy = 0.5, variance of x = 1, and the variance of y = 1.

a) find the marginal pdf of X.

b) find the marginal pdf of Y.

c) find P(X>4)

d) find E[2X + 3Y]

e) find E[(2X + 3Y)^2] (X and Y are not uncorrelated)

f) find V[2X + 3Y]

g) P(2X + 3Y < 11)

Any help is appreciated. I have some answers but I dont think they're right....

Random variables X and Y are jointly distributed with a bivariate Gaussian (Normal) distribution with E[X]=3, E[Y]=2, pxy = 0.5, variance of x = 1, and the variance of y = 1.

a) find the marginal pdf of X.

b) find the marginal pdf of Y.

c) find P(X>4)

d) find E[2X + 3Y]

e) find E[(2X + 3Y)^2] (X and Y are not uncorrelated)

f) find V[2X + 3Y]

g) P(2X + 3Y < 11)

Any help is appreciated. I have some answers but I dont think they're right....