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

1. An asset price S is lognormally distributed if:

A) ln(1+dS/S) is normally distributed
B) 1/S is normally distributed
C) ln(dS/S) is normally distributed
D) the change in price (dS) is normally distributed

2. Let a, b and c be real numbers. Which of the following statements is true?

A) The associativity of multiplication is defined by
B) The distributivity of multiplication is defined by
C) The existence of negatives is defined by
D) The commutativity of multiplication is defined by

3. Let f(x) = c for x in [0,4] and 0 for other values of x.
What is the value of the constant c that makes f(x) a probability density function; and what if f(x) = cx for x in
[0,4]?

A) 1/4 and 1/6
B) 1/7 and 1/9
C) 1/4 and 1/7
D) None of the above

4. 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) 1.3
B) -1.2
C) None of the above
D) -2.8

5. Calculate the determinant of the following matrix:

A) 2
B) -4.25
C) 4.25
D) 4

Solutions: