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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Statistics and Regression Analysis | 20% | - Linear regression
|
| Linear Algebra and Matrix Theory | 20% | - Vectors and eigenvalues
|
| Probability Theory | 25% | - Random variables and distributions
|
| Numerical Methods & Financial Mathematics | 15% | - Time value of money - Root finding and approximation - Basics of risk modeling |
| Calculus and Functions | 20% | - Multivariable calculus
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
1. For a quadratic equation, which of the following is FALSE?
A) If the discriminant is positive there are two different real solutions
B) If the discriminant is zero, there is only one solution
C) If the discriminant is negative, there are no real solutions
D) If the discriminant is negative there are two different real solutions
2. 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 variance has a Chi2-distribution
B) The estimated mean divided by the estimated variance has a t-distribution
C) The estimated mean divided by the estimated standard deviation has a t-distribution
D) The estimated mean divided by the estimated standard deviation has a Chi2-distribution
3. In statistical hypothesis tests, 'Type I error' refers to the situation in which...
A) Both null hypothesis and alternative hypothesis are accepted
B) The null hypothesis is rejected when in fact it should have been accepted
C) The null hypothesis is accepted when in fact it should have been rejected
D) Both null hypothesis and alternative hypothesis are rejected
4. Consider a binomial lattice where a security price S moves up by a factor u with probability p, or down by a factor d with probability 1 - p. If we set d > 1/u then which of the following will be TRUE?
A) The lattice will not recombine
B) None of the above
C) There will always be a downward drift in the lattice
D) The probability of an up move will not be constant
5. 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), (ii), and (iii)
B) (i) and (ii)
C) (i) and (iii)
D) (i) only
Solutions:
| Question # 1 Answer: D | Question # 2 Answer: C | Question # 3 Answer: B | Question # 4 Answer: B | Question # 5 Answer: C |
