Let Z 1 and Z 2 be two independent N(0, 1) random variables. Define where is

Let Z₁ and Z₂ be two independent N(0, 1) random variables. Define

where ρ is a real number in (−1, 1).

a. Show that X and Y are bivariate normal.

b. Find the joint PDF of X and Y.

c. Find ρ(X, Y).

Transcribed Image Text:

X = Z, Y = pZ+1-p Z,