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PRMIA 8007 Exam Syllabus Topics:

SectionObjectives
Probability and Statistics Foundations- Statistical inference
  • 1. Confidence intervals and hypothesis testing
    • 2. Estimation theory
      - Random variables and probability distributions
      • 1. Discrete and continuous distributions
        • 2. Expectation, variance, and moments
          Stochastic Processes and Time Series- Stochastic processes basics
          • 1. Markov processes
            • 2. Brownian motion (introductory level)
              - Time series analysis
              • 1. Autocorrelation and stationarity
                • 2. AR, MA, and ARMA models
                  Risk Measurement Techniques- Volatility and correlation
                  • 1. Variance-covariance methods
                    • 2. Correlation estimation techniques
                      - Value at Risk (VaR)
                      • 1. Historical simulation approach
                        • 2. Parametric and non-parametric VaR
                          Simulation and Numerical Methods- Monte Carlo simulation
                          • 1. Random number generation
                            • 2. Risk distribution 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
                              Reveal Solution  Discussion  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
                              Reveal Solution  Discussion  0

                              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
                              Reveal Solution  Discussion  0

                              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
                              Reveal Solution  Discussion  0

                              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
                              Reveal Solution  Discussion  0

                              Correct Answer: C  🗳️

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