# 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

A survey of a group's viewing habits over the last year revealed the following information:

1. 28% watched gymnastics
2. 29% watched baseball
3. 19% watched soccer
4. 14% watched gymnastics and baseball
5. 12% watched baseball and soccer
6. 10% watched gymnastics and soccer
7. 8% watched all three sports.

Calculate the percentage of the group that watched none of the three sports during the last year.

2

You are given

Determine P[A] .

3

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. Determine the probability that exactly seven claims will be received during a given two week period.

4

The stock prices of two companies at the end of any given year are modeled with random variables X and Y that follow a distribution with joint density function

What is the conditional variance of Y given that X = x ?

5

An insurer's annual weather-related loss, X, is a random variable with density function

Calculate the difference between the 30th and 70th percentiles of X.