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PRMIA 8007 Exam Syllabus Topics:

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

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

                                    1. Consider the linear regression model for the returns of stock A and the returns of stock B. Stock A is 50% more volatile than stock B. Which of the following statements is TRUE?

                                    A) The stocks must be positively correlated ( )
                                    B) Alpha must be positive ( )
                                    C) Beta must be greater in absolute value than the correlation of the stocks ( )
                                    D) Beta must be positive ( )


                                    2. Evaluate the derivative of exp(x2 + 2x + 1) at the point x = -1

                                    A) 1
                                    B) 0
                                    C) 2
                                    D) 0.5


                                    3. Find the roots, if they exist in the real numbers, of the quadratic equation

                                    A) -4 and 2
                                    B) 1 and 0
                                    C) No real roots
                                    D) 4 and -2


                                    4. An asset price S is lognormally distributed if:

                                    A) 1/S is normally distributed
                                    B) ln(1+dS/S) is normally distributed
                                    C) the change in price (dS) is normally distributed
                                    D) ln(dS/S) is normally distributed


                                    5. What is the 40th term in the following series: 4, 14, 30, 52, ...?

                                    A) 240
                                    B) 4960
                                    C) 4840
                                    D) 4598


                                    Solutions:

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

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