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.

Eliminate the parameter t: x = 1 - 4 cos t, y = -5 + 6 sin t

	A. (x-1)² / 16 + (y+5)² / 36 = 1
	B. (x-1)² / 4 + (y+5)² / 6 = 1
	C. (x+1)² / 4 + (y-5)² / 6 = 1
	D. (x+1)² / 16 + (y-5)² / 36 = 1
	E. None of the above

Which of the following statements is true?

	A. The vertex of the parabola described by f(x) = 2(x-5)² - 1 is at (5,1).
	B. The graph of f(x) = -2(x+4)² - 8 has one y-intercept and two x-intercepts.
	C. The maximum value of the quadratic function f(x) = - x² + x + 1 is 1.
	D. No quadratic function has a range of
	E. None of the above.

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}

The joint probability density function of the integer valued discrete random variables X and Y is given by

f(x,y)	= (x + y) / 60		for x =1,2,3,4 and 0 < y < x +1
	= 0		otherwise

Given that Y = 3 , calculate the probability that X = 4.

	A. 7/50
	B. 6/13
	C. 7/13
	D. 6/50
	E. 13/50

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