Jim is applying to a car insurance company for his car insurance policy. Using the probabilities that the car will have an accident in its 5th, 6th, 7th, 8th, or 9th year, and the $50,000 accident benefit, what is the expected loss to Car Insurance Company for the respective years?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Jim has a 5-year-old car in reasonably good condition. He wants to take out a $50,000 term (that is, accident benefit) car insurance policy until the car is 10 years old. Assume that the probability of a car having an accident in the year in which it is x years old is as follows:
| x = age |
5 |
6 |
7 |
8 |
9 |
P(accident)
0.01182
0.01282
0.01386
0.01513
0.01602
Jim is applying to a car insurance company for his car insurance policy. Using the probabilities that the car will have an accident in its 5th, 6th, 7th, 8th, or 9th year, and the $50,000 accident benefit, what is the expected loss to Car Insurance Company for the respective years?
We know that the expected loss is equal to the probability that a loss will occur times the cost of the loss.
Given :
| x = age | 5 | 6 | 7 | 8 | 9 |
| P(accident) | 0.01182 | 0.01282 | 0.01386 | 0.01513 | 0.01602 |
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