PRMIA : 8007 Questions & Answers

Updated: Aug 05, 2026

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PRMIA 8007 Exam Syllabus Topics:

SectionObjectives
Probability Theory- Fundamental Probability Concepts
  • 1. Probability Rules
  • 2. Random Variables
  • 3. Conditional Probability
  • 4. Bayes' Theorem
Numerical Methods- Quantitative Techniques
  • 1. Optimization Methods
  • 2. Simulation Techniques
  • 3. Monte Carlo Methods
  • 4. Numerical Approximation
Linear Algebra- Matrix Methods
  • 1. Matrix Operations
  • 2. Positive Definiteness
  • 3. Eigenvalues and Eigenvectors
  • 4. Covariance Matrices
Risk Measurement Applications- Quantitative Risk Analysis
  • 1. Volatility Modeling
  • 2. Portfolio Risk Measurement
  • 3. Value at Risk Methodologies
  • 4. Sensitivity Analysis
Statistical Analysis- Descriptive and Inferential Statistics
  • 1. Moments and Distributions
  • 2. Hypothesis Testing
  • 3. Maximum Likelihood Estimation
  • 4. Confidence Intervals
Regression and Time Series Analysis- Modeling Techniques
  • 1. Multivariate Regression
  • 2. Model Diagnostics
  • 3. Linear Regression
  • 4. Time Series Forecasting
Calculus- Differential and Integral Calculus
  • 1. Functions and Limits
  • 2. Integration
  • 3. Multivariable Calculus
  • 4. Differentiation

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

1. You want to test the hypothesis that a population parameter of a regression model is zero. Your alternative hypothesis is that 0. Denote by SD() the estimated standard deviation of , and by MEAN() the estimated mean of . Which test statistic is appropriate, and what is its distribution?

A) test statistic = SD()/MEAN(), normal distribution
B) test statistic = MEAN()/SD(), t distribution
C) test statistic = SD()/MEAN(), t distribution
D) test statistic = MEAN()/SD(), normal distribution


2. 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) 0.32
B) 1.92
C) 0.96
D) 0.64


3. Identify the type and common element (that is, common ratio or common difference) of the following sequence: 6, 12, 24

A) geometric sequence, common ratio 3
B) geometric sequence, common ratio 2
C) arithmetic sequence, common difference 2
D) arithmetic sequence, common ratio 2


4. You intend to invest $100 000 for five years. Four different interest payment options are available. Choose the interest option that yields the highest return over the five year period.

A) a lump-sum payment of $22 500 on maturity (in five years)
B) a continuously-compounded rate of 4%
C) a quarterly-compounded rate of 4.1%
D) an annually compounded rate of 4.15%


5. You are given the following values of a quadratic function f(x): f(0)=0, f(1)=-2, f(2)=-5. On the basis of these data, the derivative f'(0) is ...

A) in the interval ]-2.5,-2[
B) in the interval ]-2,+[
C) in the interval ]-,-2.5]
D) equal to -2


Solutions:

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

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