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PRMIA 8007 Exam Syllabus Topics:
| Section | Objectives |
|---|---|
| Probability and Statistics Foundations | - Statistical inference
|
| Stochastic Processes and Time Series | - Stochastic processes basics
|
| Risk Measurement Techniques | - Volatility and correlation
|
| Simulation and Numerical Methods | - Monte Carlo simulation
|
PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:
The Lagrangian of a constrained optimisation problem is given by L(x,y,) = 16x+8x2+4y-(4x+y-20), where is the Lagrange multiplier. What is the solution for x and y?
- A. x = 5, y = 0
- B. None of the above
- C. x = 0, y = 20
- D. x = -1, y = 0
Correct Answer: C 🗳️
Evaluate the derivative of exp(x2 + 2x + 1) at the point x = -1
- A. 0.5
- B. 0
- C. 2
- D. 1
Correct Answer: B 🗳️
Let X be a random variable normally distributed with zero mean and let . Then the correlation between X and Y is:
- A. not defined
- B. zero
- C. positive
- D. negative
Correct Answer: B 🗳️
Consider two functions f(x) and g(x) with indefinite integrals F(x) and G(x), respectively. The indefinite integral of the product f(x)g(x) is given by
- A. f(x)G(x) - F(x)g'(x)dx
- B. F(x)G(x)
- C. F(x)g(x) + f(x)G(x)
- D. F(x)g(x) - F(x)g'(x)dx
Correct Answer: D 🗳️
The first derivative of a function f(x) is zero at some point, the second derivative is also zero at this point. This means that:
- A. f has necessarily neither a minimum nor a maximum at this point
- B. f has necessarily a minimum at this point
- C. f might have either a minimum or a maximum or neither of them at this point
- D. f has necessarily a maximum at this point
Correct Answer: C 🗳️
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