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

2. Evaluate the derivative of exp(x2 + 2x + 1) at the point x = -1

A) 0
B) 2
C) 0.5
D) 1

3. Solve the simultaneous linear equations: x + 2y - 2 = 0 and y - 3x = 8

A) None of the above
B) x = 2, y = 0
C) x = -2, y = 2
D) x = 1, y = 0.5

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

5. Maximum likelihood estimation is a method for:

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

Solutions: