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Which is the distribution of (X,Y) ?

mathmari

Well-known member
MHB Site Helper
Apr 14, 2013
4,004
Hey!! :eek:

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)
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,684
Hey!! :eek:

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.