join distribution help

Jeonsah

New member
Joined
Feb 5, 2012
Messages
14
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
Joined
Apr 12, 2005
Messages
9,789
You have to show us D and E, first.

And F
 
Last edited:

Jeonsah

New member
Joined
Feb 5, 2012
Messages
14
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) ?
 
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