A discrete distribution occurs when a random variable has outcomes that can be listed and probabilities can be assigned between 0 and 1 in value and total to 1.

Payout for a hypothetical whole life insurance policies can provide a simple example. Imagine a policy holder can purchase a Company X whole life insurance policy to pay a death benefit to a beneficiary upon death or allows the policy holder to cash out the policy at a specified age. The payout table for the Company X whole life insurance policy is:

payoutprobability

$50,000.55(policy holder dies before cashing out the policy)

$35,000.45(policy holder is permitted to cash out the policy at the age of 80)

The expected payout is just the weighted average found by summing payout values times their corresponding probabilities. In this example the expected value would be:

$50,000*.55 + $35,000*.45 = $27,500 + $15,750= $43,250

This represents how much on average the Company X pays out on this policy.

Suppose the payout table for the Company Y whole life policy is:

payoutprobability

$50,000.45(policy holder dies before cashing out the policy)

$25,000.55(policy holder is permitted to cash out the policy at age 70)

A) Determine the expected payout for the Company Y whole life policy.

B) Even though the expected payout of Company Y is less than Company X, what may make the Company Y policy more attractive to the consumer?