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.
An insurance company issues policies to two groups of insured A and B. For a certain type of coverage, the number of claims per year for each group follows the Poisson distribution  For group A,  = 1, and for group B, = 1.5. If in calendar year 2003, 2/5 of this company's policyholders are of group A, what is the probability that the combined number of claims from both groups is no more that two.
2.
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.
3.
Eliminate the parameter t: x = 1 - 4 cos t, y = -5 + 6 sin t
4.
The joint probability density function of the integer valued discrete random variables X and Y is given by f(x,y) | = (x + y) / 60 | | for x =1,2,3,4 and 0 < y < x +1 | | = 0 | | otherwise |
Given that Y = 3 , calculate the probability that X = 4.
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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