Question

A certain insurance company charges Mike's wife $250 for a one-year $100,000 life insurance policy. Because Mike is a 21 year-old male, there is a 0.9985 probability that he'll live for a year. (U.S. National Center for Health Statistics). The probability distribution for X, the profit of Mike's wife, is:

Answer 1

Answer:

X      |    100000      -250

P(X)  |     0.0015     0.9985

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

And replacing we got:

$E(X) =100000*0.0015 -250*0.9985= -99.625$

Explanation:

For this case we define the random variable X as the profit of Mike's wife for one year on specific.

We know that the company charges $250 for one year $100000 life insurance policy

And we know that the probability that Mike would live for a year is 0.9985. So then the probability that Mike no live for a given year is 1-0.9985=0.0015

And then we can define the probability distribution like this:

X      |    100000      -250

P(X)  |     0.0015     0.9985

And we can calculate the expected value for a given year like this:

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

And replacing we got:

$E(X) =100000*0.0015 -250*0.9985= -99.625$