Normal Random Variable

Joint Normality
If two RVs $$\matbhf{x,y}$$ are jointly normal and $$\mathbf z$$ and $$\mathbf w$$ are defined as

$$\mathbf{z} = a \mathbf x + b \mathbf y\,\,\,\,\,\, \mathbf w = c \mathbf x + d \mathbf y$$,

then $$\mathbf z$$ and $$\mathbf w$$ are also jointly normal. The parameters of the joint distribution are:


 * $$\mu_z = a \mu_x + b \mu_y$$
 * $$\mu_w = c \mu_x + d \mu_y$$