Question

Consider the bivariate random vector
x =

x1
x2

∼ N2
µ1
µ2

,

σ
2
1 ρσ1σ2
ρσ1σ2 σ
2
2

1. Expand the matrix form of the density function to get the usual bivariate normal
density involving σ1, σ2, ρ and exponential terms in (x1 1µ1)
2
,(x1 1µ2) and (x2 2µ2)
2
.
2. Explain what happens in the following scenarios:
(a) ρ = 0
(b) ρ = 1
(c) ρ = =1
1

Answer 1