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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Linear Algebra and Matrix Theory | 20% | - Vectors and eigenvalues
|
| Numerical Methods & Financial Mathematics | 15% | - Basics of risk modeling - Root finding and approximation - Time value of money |
| Probability Theory | 25% | - Random variables and distributions
|
| Statistics and Regression Analysis | 20% | - Linear regression
|
| Calculus and Functions | 20% | - Single-variable calculus
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
What can be said about observations of random variables that are i.i.d. a normally distributed?
- A. The estimated mean divided by the estimated standard deviation has a Chi2-distribution
- B. The estimated mean divided by the estimated standard deviation has a t-distribution
- C. The estimated mean divided by the estimated variance has a Chi2-distribution
- D. The estimated mean divided by the estimated variance has a t-distribution
Correct Answer: B 🗳️
The correlation between two asset returns is 1. What is the smallest eigenvalue of their correlation matrix?
- A. 0
- B. None of the above
- C. 0.5
- D. 1
Correct Answer: A 🗳️
You want to test the hypothesis that a population parameter of a regression model is zero. Your alternative hypothesis is that 0. Denote by SD() the estimated standard deviation of , and by MEAN() the estimated mean of . Which test statistic is appropriate, and what is its distribution?
- A. test statistic = SD()/MEAN(), normal distribution
- B. test statistic = MEAN()/SD(), normal distribution
- C. test statistic = SD()/MEAN(), t distribution
- D. test statistic = MEAN()/SD(), t distribution
Correct Answer: D 🗳️
An operational risk analyst models the occurrence of computer failures as a Poisson process with an arrival rate of 2 events per year. According to this model, what is the probability of zero failures in one year?
- A. 0.50
- B. 0.02
- C. 0.25
- D. 0.14
Correct Answer: D 🗳️
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. -1.2
- B. None of the above
- C. -2.8
- D. 1.3
Correct Answer: A 🗳️
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