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.

For insurance company ABC the proportion of claims p, which remains unpaid two weeks after claims are reported, follows the following probability density function

f(p) = k p(1-p)⁶ for 0< p < 1

Calculate k.

	A. 8/3
	B. 3/8
	C. 56
	D. 1/56
	E. 42

Sales, S, of a new insurance product are dependent upon the labor, L, of the sales force and the amount of advertising, A, for the product. The relationship can be modeled by

Which of the following statements is true?

	A. S increases at an increasing rate as L increases, and increases at a decreasing rate as A increases.
	B. S increases at an increasing rate as L increases, and increases at an increasing rate as A increases.
	C. S increases at a decreasing rate as L increases, and increases at a decreasing rate as A increases.
	D. S increases at a decreasing rate as L increases, and increases at an increasing rate as A increases.
	E. S increases at a constant rate as L increases, and increases at a constant rate as A increases.

In calendar year 2003, the medical claim costs per employee of a company is estimated to have the following probability density function:

f(x) = k × e^{- x / 2} x > 0

where k is a constant that you need to calculate, and x is in units of $1000.

What is the probability that costs per employee in 2003 will exceed $6000.

	A. 0.993
	B. 0.954
	C. 0.199
	D. 0.801
	E. 0.503

The joint probability density function of yearly returns for two investments A and B is given below:

Calculate the covariance of returns on A and B.

	A. 0.003450
	B. 0.001747
	C. 0.001764
	D. 0.000538
	E. 0.005380

The number of items produced by a manufacturer is given by p = 100 , where x is the amount of capital and y is the amount of labor. At a particular point in time:

(i)     the manufacturer has 2 units of capital,
(ii)     capital is increasing at a rate of 1 unit per month,
(iii)     the manufacturer has 3 units of labor, and
(iv)     labor is decreasing at a rate of 0.5 units per month.

Determine the rate of change in the number of items produced at the given time.

	A. 41
	B. 61
	C. 82
	D. 102
	E. 245