Let X and Y be two jointly normal random variables with X N(X,X), Y N( Y , Y ), and (X, Y)

Let X and Y be two jointly normal random variables with X ∼ N(μX,σX), Y ∼ N(μ_Y, σ_Y), and ρ(X, Y) = ρ. Show that the above PDF formula for PDF of [X Y] is the same as f_X,Y (x, y) given in Definition 5.4 in Section 5.3.2. That is,

fxr(x,y) 1 2V1 - 1 - My pra-p|(***)* +(*=#r)* 2(1 p) exp 2 2 (x )(y - ) - 20- *)]}.