In: Statistics and Probability
An insurance company is considering offering fire insurance to customers in a certain state. After examining thousands of records of insurance claims in the area, they have come up with the following information:
Payout | Number of Claims |
$58,971 | 22 |
28,117 | 602 |
0 | 2,972 |
First convert the table into a probability distribution by dividing each number in the "Claims" column by the total number of claims. Take probability calculations to 3 decimal places.
Now, let X be the expected payout. Find E(X), the expected value of X, to two decimal places.
Payout (X) | Number of claims | Probability distribution (p) |
58971 | 22 | 22 / 3596 = 0.006 |
28117 | 602 | 602 /3596 = 0.167 |
0 | 2972 | 2972 / 3596 = 0.827 |
Total number of claims = 22 + 602 + 2972 = 3596
E(X) =
= 0.006 * 58971 + 0.167 * 28117 + 0.827 * 0
= 5049.37