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

1. ## 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).

2. 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.

3. 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