# bivariate normal distribution - how do I even do this?

• Oct 17th 2010, 06:56 PM
Sneaky
bivariate normal distribution - how do I even do this?
The bivariate distribution: Bivariate Normal Distribution -- from Wolfram MathWorld

The question states:

Let X and Y have the bivariate normal (3,5,2,4,0.5) distribution.
a)Specify the marginal distribution of X.
b)Specify the marginal distribution of Y.

I have no idea how to do this. Can someone help?

From my book the only thing I could establish was
X=3+2Z
Y=5+4(Z/2 + C*sqrt(3/4))
where Z and C are independent random variables, both distributed N(0,1).
• Oct 17th 2010, 07:10 PM
nehme007
If I'm interpreting your notation properly, you can read off the marginal distributions using the parameters of the bivariate distribution. If X and Y are jointly bivariate normal, then each of X and Y is normally distributed. You simply need to specify the mean and variance for each. If I'm reading this properly, X has mean 3 and variance 2, and Y has mean 5 and variance 4. I'm guessing the 0.5 is either the covariance or correlation, but this doesn't impact the marginals.
• Oct 17th 2010, 07:16 PM
Sneaky
I'm still not sure how to properly write the marginal distribution of X and Y.

the notation of
(3,5,2,4,0.5)
is
(u1,u2,sigma1,sigma2,p)

p is the correlation