Surety Life Insurance Co. is just starting out, and so far has written only one policy.   This policy will pay the company a premium of $2,500 next year, with certainty. However, there is a 0.2% chance that the insured will expire, and the company will have to pay a $1 million death benefit on the policy before the year is over.

(a) List the probability distribution for Surety’s cash flow over the next year.

(b) Compute Surety’s expected cash flow and standard deviation of cash flow over the next year.

Assume now that Surety has written two smaller policies instead of the single policy described earlier. Each policy will pay Surety $1250 next year with certainty.   The death benefit on each policy is $0.5 million. The probability of paying the death benefit is 0.2% for each policy, and the payouts on the two policies are statistically independent (implying that the correlation is zero).   (Useful fact – the probability of a pair of independent events both occurring is the product of the individual probabilities.)  

(c) List the probability distribution for Surety’s cash flow over the next year.

(d) Compute Surety’s expected cash flow and standard deviation of cash flow over the next year.

(e) Explain the principle illustrated by comparing answers to parts (b) and (d).