# join distribution help

#### Jeonsah

##### New member
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....

#### tkhunny

##### Moderator
Staff member
You have to show us D and E, first.

And F

Last edited:

#### Jeonsah

##### New member
By showing you those, do you mean my work? or what they gave in the problem?

They did not give anything else other than what I have posted.

Heres my answers so far:

a) fx(x) = [1/sqrt(2pi)] * exp-((x-3)^2/2)
b) same thing as a. but y instead of X.
c) 0.158655???
d)12
e) I got here:
4E[X^2] + 12E[XY] + 9E[Y^2]
I dont know what to do with 12E[XY]

f) 5
g) ?