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PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:

1. Which of the following properties is exhibited by multiplication, but not by addition?

A) distributivity
B) commutativity
C) invertibility
D) associativity

2. The fundamental theorem of analysis establishes a relation between

A) First and second derivative of a function
B) The derivative of a function and the slope of its graph
C) Integration and differentiation of functions
D) The derivative of a function and the derivative of its inverse function

3. Let E(X ) = 1, E(Y ) = 3, Corr(X, Y ) = -0.2, E(X2 ) = 10 and E(Y2 ) = 13. Find the covariance between X and Y

A) None of the above
B) -1.2
C) 1.3
D) -2.8

4. What is the total derivative of the function f(x,y) = ln(x+y), where ln() denotes the natural logarithmic function?

A) ln(x+y) x + ln(x+y) y
B) (x + y) / (x+y)
C) -x/(x+y) - y/(x+y)
D) 1 / (x+y)

5. The determinant of a matrix X is equal 2. Which of the following statements is true?

A) det(2X) =
B) det(2X) = det(X)2
C) det(2X) = 2 det(X)
D) det(2X) = 4 det(X)

Solutions: