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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Statistics and Regression Analysis | 20% | - Linear regression
|
| Probability Theory | 25% | - Random variables and distributions
|
| Calculus and Functions | 20% | - Multivariable calculus
|
| Linear Algebra and Matrix Theory | 20% | - Vectors and eigenvalues
|
| Numerical Methods & Financial Mathematics | 15% | - Time value of money - Root finding and approximation - Basics of risk modeling |
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
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
Correct Answer: D 🗳️
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
Correct Answer: C 🗳️
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
Correct Answer: B 🗳️
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
Correct Answer: B 🗳️
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
Correct Answer: C 🗳️
