Question

1. a term life insurance policy will pay a fixed sum of money to a beneficiary if the policyholder dies. a 55 - year old man can buy a $250,000 term life policy for $450/year. suppose that, according to actuarial tables, there is a 0.0032 this 55 - year old man will die in 2029. in the probability distribution table below, x represents the monetary gain/loss to insurance company providing term life to this man in 2029. round to 4 decimals.

	x	p(x)
if the man lives	$450

a. fill in the blank in the probability table above.
b. compute the expected value of this policy for the insurance company. does the company expect to profit by selling this policy to this man?

Explanation:

Step1: Find the missing probability

The sum of all probabilities in a probability - distribution must equal 1. Let the probability that the man lives be $P$. We know that the probability that the man dies is $0.0032$. So, $P = 1 - 0.0032$.
$P=1 - 0.0032=0.9968$

Step2: Calculate the expected value

The formula for the expected value $E(X)$ of a discrete random variable is $E(X)=\sum_{i}x_{i}P(x_{i})$. Here, $x_1=- 249550$ with $P(x_1) = 0.0032$ and $x_2 = 450$ with $P(x_2)=0.9968$.
$E(X)=(-249550)\times0.0032 + 450\times0.9968$
$E(X)=-249550\times0.0032+450\times0.9968=-798.56 + 448.56$
$E(X)=-350$

Answer:

a. $0.9968$
b. The expected value of the policy for the insurance company is $- 350$. The company does not expect to profit by selling this policy to this man.