To prove Theorem 6 10, show that if X and Y have a bivariate normal distribution, then (a) Their independence implies that 0 (b) 0 implies that they are independent Theorem 6 10 If two random variables have a bivariate normal distribution, they are independent if and only if 0 ...

a Constant terms of gx and hy are 1 1 ...

To prove Theorem 6.10, show that if X and Y have a bivariate normal distribution, then (a)

Question:

To prove Theorem 6.10, show that if X and Y have a bivariate normal distribution, then
(a) Their independence implies that ρ = 0;
(b) ρ = 0 implies that they are independent.
Theorem 6.10
If two random variables have a bivariate normal distribution, they are independent if and only if ρ = 0.