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Solve Real Problems

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.

1

You are given

Determine P[A] .

2

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 .

What is the probability that the device fails during its first hour of operation?

3

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) = 1 / 6
P(X = 1, Y = 0) = 1/12
P(X = 1, Y = 1) = 1 /6
P(X = 2, Y = 0) = 1 /12
P(X = 2, Y = 1) = 1 /3
P(X = 2, Y = 2) = 1/6

What is the variance of X?

4

An auto insurance company insures an automobile worth 15,000 for one year under a policy with a 1,000 deductible. During the policy year there is a 0.04 chance of partial damage to the car and a 0.02 chance of a total loss of the car. If there is partial damage to the car, the amount X of damage (in thousands) follows a distribution with density function

What is the expected claim payment?

5
An insurance policy pays for a random loss X subject to a deductible of C, where 0 < C < 1. The loss amount is modeled as a continuous random variable with density function

Given a random loss X, the probability that the insurance payment is less than 0.5 is equal to 0.64 .

Calculate C.