Question

Life tables show that the probability a healthy 23-year-old man will die before his 30th birthday is 0.065. Suppose one insurance company is considering offering a life insurance policy for men who have just turned 23. The policy will pay $150,000 if the policy holder dies before his 30th birthday, nothing if he does not. The premium, which has to be paid at the time the policy is purchased, will be set at $1000. Create the table that shows the company’s net payouts and the probabilities for those payouts, and find the expected net payout per policy.

Answer 1

Solution

Back-up Theory

If a discrete random variable, X, has probability function, p(x), x = x₁, x₂, …., x_n, then

Expected value = Σ{x.p(x)} summed over all possible values of x…................................................................…. (1)

Now, to work out the solution,

Pay-out = 150,000 if the policy holder dies before his 30th birthday

           = 0, if the policy holder survives upto his 30th birthday

Pay-out - x	Probability – p(x)	x.p(x)
150000	0.065	9750
0	0.935	0
Total	1.000	9750

So, vide (1), expected net payout per policy = $9750 Answer

Since premium of 1000 per policy is a revenue, expected net loss per policy = $8750

DONE