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

[mathmari]

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 $Y$ ? (Wondering)

 

[I like Serena]

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! (Wave)

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

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.