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PRMIA 8007 Exam Syllabus Topics:

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

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

                                    1. What is the simplest form of this expression: log2(165/2)

                                    A) log2 (5/2) + log2(16)
                                    B) 10
                                    C) 5/2 + log2(16)
                                    D) 32


                                    2. Let A be a square matrix and denote its determinant by x. Then the determinant of A transposed is:

                                    A) x
                                    B) -x
                                    C) ln(x)
                                    D) x -1


                                    3. The sum of the infinite series 1+1/2+1/3+1/4+1/5+.... equals:

                                    A) 20
                                    B) 128
                                    C) Infinity
                                    D) 12


                                    4. In a quadratic Taylor approximation, a function is approximated by:

                                    A) a straight line
                                    B) a cubic polynomial
                                    C) a parabola
                                    D) a constant


                                    5. 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) [0, 1.5]
                                    B) None of the above
                                    C) [1, 2]
                                    D) [0, 3]


                                    Solutions:

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

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