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PRMIA 8007 Exam Syllabus Topics:

SectionWeightObjectives
Numerical Methods & Financial Mathematics15%- Root finding and approximation
- Time value of money
- Basics of risk modeling
Calculus and Functions20%- Single-variable calculus
  • 1. Integrals and applications
    • 2. Limits and continuity
      • 3. Derivatives and applications
        - Multivariable calculus
        • 1. Optimization
          • 2. Partial derivatives
            Linear Algebra and Matrix Theory20%- Matrix operations
            • 1. Addition, multiplication, inversion
              • 2. Determinants and trace
                - Vectors and eigenvalues
                • 1. Diagonalization
                  • 2. Eigenvalues and eigenvectors
                    Statistics and Regression Analysis20%- Linear regression
                    • 1. Simple and multiple regression
                      • 2. Hypothesis testing and confidence intervals
                        - Descriptive statistics
                        • 1. Correlation and covariance
                          • 2. Measures of location and dispersion
                            Probability Theory25%- Random variables and distributions
                            • 1. Expected value, variance, covariance
                              • 2. Discrete and continuous distributions
                                - Basic probability concepts
                                • 1. Conditional probability and independence
                                  • 2. Axioms and rules

                                    PRMIA Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition Sample Questions:

                                    1. What is the maximum value for f(x)= 8-(x+3)(x-3)?

                                    A) -1
                                    B) 8
                                    C) None of these
                                    D) 17


                                    2. Which of the following is a false statement concerning the probability density function and the cumulative distribution function of a random variable?

                                    A) the PDF is non-negative.
                                    B) the definite integral of the CDF from minus infinity to plus infinity is undefined.
                                    C) the CDF approaches 1 as its argument approaches infinity.
                                    D) the definite integral of the PDF from minus infinity to plus infinity is zero.


                                    3. A linear regression gives the following output:
                                    Figures in square brackets are estimated standard errors of the coefficient estimates.
                                    Which of the following is an approximate 95% confidence interval for the true value of the coefficient of ?

                                    A) None of the above
                                    B) [0, 3]
                                    C) [0, 1.5]
                                    D) [1, 2]


                                    4. You are investigating the relationship between weather and stock market performance. To do this, you pick
                                    100 stock market locations all over the world. For each location, you collect yesterday's mean temperature and humidity and yesterday's local index return. Performing a regression analysis on this data is an example of...

                                    A) Multiple time-series regression
                                    B) Simple cross-section regression
                                    C) Multiple cross-section regression
                                    D) Simple time-series regression


                                    5. A linear regression gives the following output:
                                    Figures in square brackets are estimated standard errors of the coefficient estimates.
                                    What is the value of the test statistic for the hypothesis that the coefficient of is less than 1?

                                    A) 0.96
                                    B) 1.92
                                    C) 0.32
                                    D) 0.64


                                    Solutions:

                                    Question # 1
                                    Answer: D
                                    Question # 2
                                    Answer: D
                                    Question # 3
                                    Answer: B
                                    Question # 4
                                    Answer: C
                                    Question # 5
                                    Answer: D

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