# Which is the distribution of (X,Y) ?

#### mathmari

##### Well-known member
MHB Site Helper
Hey!!

We have that $X$ and $Y$ follow the normal distribution $N(0,1)$ and are independent.
1. Which is the distribution of $(X,Y)$ ?
2. Which is the covariance table of $(X,Y)$ ?

Is $(X,Y)$ related to the linear combination of $X$ and $Y$ ?

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Hey!!

We have that $X$ and $Y$ follow the normal distribution $N(0,1)$ and are independent.
1. Which is the distribution of $(X,Y)$ ?
2. Which is the covariance table of $(X,Y)$ ?

Is $(X,Y)$ related to the linear combination of $X$ and $Y$ ?
Hey mathmari !!

It's a so called Bivariate normal distribution.
The section in the wiki article explains how to get the covariance table.

And no, $(X,Y)$ is not linear combination of $X$ and $Y$.
However, a property of a bivariate normal distribution is that any linear combination $\lambda X + \mu Y$ has a normal distribution.