Online Exam: College
Actuaries in the U.S., Canada and other parts of the world earn professional credentials by passing a series of examinations. This Online Exam is designed to give you an idea of the types of questions you might encounter on the preliminary actuarial examinations administered by the Casualty Actuarial Society and Society of Actuaries. Please be sure to review the Actuarial Exams section of the Web Site, where you can access complete sample actuarial exams.
Answer the five multiple choice questions below, then click submit to see your results. If you are a high school student, please take our High School version of the Online Exam.
1.
The joint probability density function of the loss amount X, and the expenses associated with that loss Y, is given by f(x,y) = 4 e -2(x+y) for x>0, y>0. Assuming an insurance policy is written to reimburse the total amount of loss plus expense X+Y, calculate the probability that the reimbursement would be less than 1.
2.
Which of the following statements is true?
3.
For each policy the distribution of fire losses is given below: Loss amount | | Probability |
| 0 | | 0.9 | 100 | 0.05 | 500 | 0.03 | 1000 | 0.01 | 10000 | 0.01 |
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Calculate insurer's expected payment, for policies written with a deductible of $100.
4.
An insurance company has 150,000 to spend on the development and promotion of a new insurance policy for renters. If x is spent on the development and y is spent on the promotion,  policies will be sold. Calculate the maximum sales, in thousands, the company can attain.
5.
In calendar year 2002 the claim costs for a particular coverage follow an unspecified distribution with mean equal to $5,000 and variance equal to $2,000,000. Assume that claim cost inflation is 5 percent per year. Calculate the standard deviation of claim costs in 2004 rounded to the nearest dollar.
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