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.

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

Ten percent of an insurance company's policyholders had at least one claim in the past five years. The rest had none.

For each policyholder who had at least one claim in the past five years, the probability of having a claim this year is 0.15. For the rest, the probability of having a claim is 0.05.

Given that a policyholder has a claim this year, what is the probability that this policyholder had at least one claim in the past five years.

	A. 0.0150
	B. 0.1500
	C. 0.7500
	D. 0.4375
	E. 0.2500

The telephone numbers in a certain area all start with 4 and then 3. The third digit can be 7,8, or 9. Each of the last four digits can be any number from 0 to 9. There are 28,243 telephone numbers assigned in the area. How many phone numbers are still unassigned?

	A. 28,243
	B. 30,000
	C. 331,757
	D. 1,757
	E. None

Evaluate the following integral given that A is the region bounded by x = 0, y = 0, and x + y = 1.

× e^-(x+2y) dx dy
A

	A. 3(1-e^-2)/8
	B. 3(1-e^-1)/8
	C. (1-e^-1)²/2
	D. (1-e^-1)²
	E. None of the above

Let be a sequence of real numbers.

For which of the following does the infinite series converge?

	A.
	B.
	C.
	D.
	E.