An insurance agent likes to sell two types of policies to his clients, selling them both life insurance and auto insurance. The following joint distribution summarizes the properties of the number of...

An insurance agent likes to sell two types of policies to his clients, selling them both life insurance and auto insurance. The following joint distribution summarizes the properties of the number of life insurance policies sold to an individual () and the number of auto policies ().

(a) Find the expected value and variance of the number of life insurance policies.

(b) Find the expected value and variance of the number of auto insurance policies.

(c) Find and interpret
 in the context of this problem.

(d) Find the correlation between
 and
. (Hint: You can use the alternative formula for the covariance shown in the Formulas section at the end of the chapter.)

(e) Interpret the size of the correlation for the agent.

(f) The agent earns $750 from selling a life insurance policy and $300 from selling an auto policy. What is the expected value and standard deviation of the earnings of this agent from policies sold to a client?