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

1. 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) -2.8
C) -1.2
D) None of the above

2. At what point x does the function f(x) = x3 - 4x2 + 1 have a local minimum?

A) 0
B) 2.66667
C) -0.666666667
D) 2

3. What is the maximum value of the function F(x, y)=x2+y2 in the domain defined by inequalities x 1, y -2, y-x 3 ?

A) 29
B) 17
C) -25
D) 1

4. Which of the following statements is true?

A) The constant plays an important role in the mathematical description of continuous compounding.
B) Continuous compounding is the better method because it results in higher present values compared to discrete compounding.
C) Discrete and continuous compounding produce the same results if the discount rate is positive.
D) Continuous compounding can be thought as making the compounding period infinitesimally small.

5. Maximum likelihood estimation is a method for:

A) Solving a portfolio optimization problem
B) Estimating the implied volatility of a simple European option
C) Finding parameter estimates of a given density function
D) Estimating the solution of a partial differential equation

Solutions: