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PRMIA 8007 Exam Syllabus Topics:
| Section | Weight | Objectives |
|---|---|---|
| Linear Algebra and Matrix Theory | 20% | - Vectors and eigenvalues
|
| Probability Theory | 25% | - Basic probability concepts
|
| Numerical Methods & Financial Mathematics | 15% | - Time value of money - Basics of risk modeling - Root finding and approximation |
| Statistics and Regression Analysis | 20% | - Descriptive statistics
|
| Calculus and Functions | 20% | - Multivariable calculus
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
A simple linear regression is based on 100 data points. The total sum of squares is 1.5 and the correlation between the dependent and explanatory variables is 0.5. What is the explained sum of squares?
- A. 0.375
- B. 0.3333
- C. 0.75
- D. 1.125
Correct Answer: A 🗳️
The gradient of a function f(x, y, z) = x + y2 - x y z at the point x = y = z = 1 is
- A. (0, 1, -1)
- B. (0, 2, 1)
- C. (1, 1, 1)
- D. (0, 0, 0)
Correct Answer: A 🗳️
A bond has modified duration 6 and convexity 30. Find the duration-convexity approximation to the percentage change in bond price when its yield increases by 5 basis points
- A. 30 basis points fall.
- B. 24 basis point rise
- C. 10 basis point rise
- D. 24 basis fall
Correct Answer: A 🗳️
For each of the following functions, indicate whether its graph is concave or convex:
Y = 7x2 + 3x + 9
Y = 6 ln(3x)
Y = exp(-4x)
- A. convex, convex, concave
- B. convex, concave, concave
- C. concave, convex, convex
- D. concave, concave, concave
Correct Answer: B 🗳️
What is the angle between the following two three dimensional vectors: a=(1,2,3), b=(-4,2,0)?
- A. 180 degrees
- B. 45 degrees
- C. 90 degrees
- D. 57 degrees
Correct Answer: C 🗳️
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