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## Apply your math skills to actuarial exam questions.

Actuaries 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. The sample problems are actual questions from prior exams, but they do not cover all the topics or all levels of difficulty.

Answer the five multiple choice questions below, then click submit to see your results.

• An insurance company determines that N, the number of claims received in a week, is a random variable with P[N = n] = 1/2n+1, where n > 0 . The company also determines that the number of claims received in a given week is independent of the number of claims received in any other week.

• A device runs until either of two components fails, at which point the device stops running.  The joint density function of the lifetimes of the two components, both measured in hours, is

f (x,y)=x+y/8 for 0< x < 2 and 0< y < 2 .

• A car dealership sells 0, 1, or 2 luxury cars on any day. When selling a car, the dealer also tries to persuade the customer to buy an extended warranty for the car. Let X denote the number of luxury cars sold in a given day, and let Y denote the number of extended warranties sold.
P(X = 0, Y = 0) = / 6
P(X = 1, Y = 0) = 1/12
P(X = 1, Y = 1) = /6
P(X = 2, Y = 0) = /12
P(X = 2, Y = 1) = /3
P(X = 2, Y = 2) = 1/6

• A company takes out an insurance policy to cover accidents that occur at its manufacturing plant. The probability that one or more accidents will occur during any given month is 3/5.

The number of accidents that occur in any given month is independent of the number of accidents that occur in all other months.