# 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.

(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.

## Answer to relevant Questions

If the exponent of e of a bivariate normal density is –1/54 (x2 + 4y2 + 2xy+ 2x+ 8y+ 4) Find σ1, σ2, and ρ, given that µ1 = 0 and µ2 = –1. In certain experiments, the error made in determining the density of a substance is a random variable having a uniform density with α = – 0.015 and β = 0.015. Find the probabilities that such an error will (a) Be ...The number of planes arriving per day at a small private airport is a random variable having a Poisson distribution with λ = 28.8. What is the probability that the time between two such arrivals is at least 1 hour? Find z if the standard- normal-curve area (a) Between 0 and z is 0.4726; (b) To the left of z is 0.9868; (c) To the right of z is 0.1314; (d) Between – z and z is 0.8502. Suppose that the actual amount of instant coffee that a filling machine puts into “6-ounce” jars is a random variable having a normal distribution with σ = 0.05 ounce. If only 3 percent of the jars are to contain less ...Post your question

0