Suppose a life insurance company sells a $260 comma 000 one-year term life insurance policy to a 25-year-old female for $230. The probability that the female survives the year is 0.999572. Compute and interpret the expected value of this policy to the insurance company.

The probability of no survive by the complement rule is

And the expected value would be given by:

So then the company would expect a net amount of 118.621 for the insurance.  

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.

The expected value is defined by this formula:

Where represent the possible values for the random variable and the corresponding probabilities.

Solution to the problem

For this case we define X a random variable who represent the net amount of money for the company.

The probability of no survive by the complement rule is

And the expected value would be given by:

So then the company would expect a net amount of 118.621 for the insurance.  

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