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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Numerical Methods & Financial Mathematics | 15% | - Root finding and approximation - Basics of risk modeling - Time value of money |
| Calculus and Functions | 20% | - Single-variable calculus
|
| Linear Algebra and Matrix Theory | 20% | - Vectors and eigenvalues
|
| Statistics and Regression Analysis | 20% | - Linear regression
|
| Probability Theory | 25% | - Basic probability concepts
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
Let X be a random variable distributed normally with mean 0 and standard deviation 1. What is the expected value of exp(X)?
- A. E(exp(X)) = 2.7183
- B. E(exp(X)) = 1.6487
- C. E(exp(X)) = 0.6065
- D. E(exp(X)) = 1
Correct Answer: B 🗳️
Two vectors are orthogonal when:
- A. their determinant is zero
- B. one is a scalar multiple of the other
- C. their scalar product (sum product) is zero
- D. their components are linearly dependent
Correct Answer: C 🗳️
You are given the following regressions of the first difference of the log of a commodity price on the lagged price and of the first difference of the log return on the lagged log return. Each regression is based on 100 data points and figures in square brackets denote the estimated standard errors of the coefficient estimates:
Which of the following hypotheses can be accepted based on these regressions at the 5% confidence level (corresponding to a critical value of the Dickey Fuller test statistic of - 2.89)?
- A. The commodity prices are stationary
- B. The commodity returns are integrated of order 1
- C. None of the above
- D. The commodity returns are stationary
Correct Answer: C 🗳️
A linear regression gives the following output:
Figures in square brackets are estimated standard errors of the coefficient estimates.
Which of the following is an approximate 95% confidence interval for the true value of the coefficient of ?
- A. [0, 1.5]
- B. [0, 3]
- C. [1, 2]
- D. None of the above
Correct Answer: B 🗳️
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 1/7
- B. 1/7 and 1/9
- C. 1/4 and 1/6
- D. None of the above
Correct Answer: D 🗳️
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