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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Probability Theory | 25% | - Random variables and distributions
|
| Calculus and Functions | 20% | - Multivariable calculus
|
| Statistics and Regression Analysis | 20% | - Descriptive statistics
|
| Numerical Methods & Financial Mathematics | 15% | - Root finding and approximation - Time value of money - Basics of risk modeling |
| Linear Algebra and Matrix Theory | 20% | - Vectors and eigenvalues
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
Question 1
In a quadratic Taylor approximation, a function is approximated by:
A. a constant
B. a parabola
C. a cubic polynomial
D. a straight line
Question 2
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 stationary
C. None of the above
D. The commodity returns are integrated of order 1
Question 3
A 95% confidence interval for a parameter estimate can be interpreted as follows:
A. The probability that the real value of the parameter is outside this interval is 95%.
B. The probability that the estimated value of the parameter is outside this interval is 95%.
C. The probability that the real value of the parameter is within this interval is 95%.
D. The probability that the estimated value of the parameter is within this interval is 95%.
Question 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. -2.8
B. 1.3
C. None of the above
D. -1.2
Question 5
Let N(.) denote the cumulative distribution function of the standard normal probability distribution, and N' its derivative. Which of the following is false?
A. N(x) 0 as x
B. N'(x) 0 as x
C. N'(0) 0
D. N(0) = 0.5
Solutions:
| Question 1 Answer: B | Question 2 Answer: C | Question 3 Answer: C | Question 4 Answer: D | Question 5 Answer: A |
