Question

A thirty year old women decides to pay $300 for a one-year life insurance policy with coverage of $100,000. The probability of her living through the year is 0.9976. What is her expected value for the insurance policy?

Answer 1

Answer:

$E(X) = 100000*(0.0024) -300*0.9976 =-59.28$

So then the expected value for this case on the year described for the woman is --$59.28, and that means a net loss.

Step-by-step explanation:

Previous concepts

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

Solution to the problem

For this case the woman needs to pay $300 for a one year life insurance and we know that the probability that she will live the year is 0.9976. So then the probability that she not live on the year is 1-0.9976=0.0024 by the complement rule , and on this case the company needs to pay 100000 for the life insurance.

So then we can use the definition of expected value given by:

$E(X) =\sum_{i=1}^n X_i P(X_i)$

And replacing the values given we have:

$E(X) = 100000*(0.0024) -300*0.9976 =-59.28$

So then the expected value for this case on the year described for the woman is --$59.28, and that means a net loss.