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

1. The gradient of a smooth function is

A) infinite at a maximum point
B) matrix of second partial derivatives of a function
C) a matrix containing the function's second partial derivatives
D) a vector that shows the direction of fastest change of a function

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

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

3. Which of the following statements are true about Maximum Likelihood Estimation?
(i) MLE can be applied even if the error terms are not i.i.d. normal.
(ii) MLE involves integrating a likelihood function or a log-likelihood function.
(iii) MLE yields parameter estimates that are consistent.

A) (i) only
B) (i) and (ii)
C) (i), (ii), and (iii)
D) (i) and (iii)

4. Bond convexity is closely related to ...

A) The integral of the bond's present value with respect to yield
B) The sensitivity of the bond's present value with respect to yield
C) The derivative of the bond's present value with respect to yield
D) The second derivative of the bond's present value with respect to yield

5. Which of the provided answers solves this system of equations?
2y - 3x = 3y +x
y2 + x2 = 68

A) x = 1; y = square root of 67
B) x = 2; y = 8
C) x = 2; y = -8
D) x = -2; y = -8

Solutions: