# Question: To prove Theorem 6 10 show that if X and Y

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.

(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.

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