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 the loss amount X, and the expenses associated with that loss Y, is given by

f(x,y) = 4 e ^-2(x+y) for x>0, y>0.

Assuming an insurance policy is written to reimburse the total amount of loss plus expense X+Y, calculate the probability that the reimbursement would be less than 1.

	A. 1 + e^-2
	B. 1 - 2 e^{- 2}
	C. 1 - 3 e^{- 2}
	D. 2 - 4 e^{- 2}
	E. 1 + 3 e^{- 2}

Given that A, B, and C are invertible matrices of correct dimensions for the stated operations and ( ' ) denote transpose, which of the following statements is not an identity?

	A. (A+B)' = A' + B'
	B. (ABC)' = C'B'A'
	C. (AB)^-1 = A^-1 B^-1
	D. (AB)^-1 = B^-1 A^-1
	E. (A')^-1 = (A^-1)'

Let be a sequence of real numbers.

For which of the following does the infinite series converge?

	A.
	B.
	C.
	D.
	E.

In calendar year 2002 the claim costs for a particular coverage follow an unspecified distribution with mean equal to $5,000 and variance equal to $2,000,000. Assume that claim cost inflation is 5 percent per year.

Calculate the standard deviation of claim costs in 2004 rounded to the nearest dollar.

	A. $1,485
	B. $1,449
	C. $1,559
	D. $4,696
	E. $5,250

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