This is the fifth post about the Companion and Self-Testing Question List for my recent book Business Risk and Simulation Modelling in Practice: Using Excel, VBA and @RISK. As mentioned in earlier posts, the complete list of questions posted in this series will also shortly be available for free on the John Wiley web-site.

As a reminder, the full series of posts correspond to the Chapters of the book as follows:

- Post I: Risk Assessment Context and Processes (Chapters 1 and 2 of book)
- Post II: Risk Assessment, Quantification and Modelling: Approaches, Benefits and Challenges (Chapters 3, 4 and 5)
- Post III: Principles of Simulation Methods (Chapter 6)
- Post IV: Core Principles in the Design of Risk Models (Chapter 7)
- Post V: Measuring Risk using Statistics of Distributions (Chapter 8)
- Post VI: The Selection of Distributions for Use in Risk Models (Chapters 9 and 10)
- Post VII: Modelling Dependencies between Sources of Risk (Chapter 11)
- Post VIII: Using Excel/VBA for Simulation Modelling (Chapter 12)
- Post IX: Using @RISK for Simulation Modelling (Chapter 13)

This is Post V, Measuring Risk using Statistics of Distributions (Chapter 8):

- What is the role and meaning of probability distributions in risk modelling?

- What is meant by context-specific risk measurement? Provide at least two simple examples.
- When such terms are distinguished from each other, what it is often meant by the terms,
*risk, variability*and*uncertainty*? - How can use of the terms uncertainty (rather than risk) sometimes help to ensure that the frame of consideration of a problem is not made too narrow?
- What are the key statistical measures that are often required to quantify the risk? Provide examples (of questions and the corresponding context) to which some of these measures correspond.
- What is meant by the density and cumulative forms of a distribution function?
- What is meant by the ascending and descending (cumulative) forms of a distribution? When may the use of one be more favorable than the use of the other?
- What is meant by discrete, continuous, and compound distributions?
- Describe how the inversion of a cumulative distribution function is required in order to create random samples from it.
- What is meant by the mean, median and mode of a distribution? When are these measures identical to each other? What are the key uses and meanings of each?
- What is meant by the standard deviation of a set of data or a distribution? What rules of thumb apply to the meaning of the standard deviation to assess the frequency of outcomes, and when are such rules not so reliable?
- What measures of the range or spread of a distribution are possible, in addition to the standard deviation? What are the advantages or disadvantages of these?
- How is the skewness of a set of data or distribution defined? What are the dimensions associated with this number?
- Does a symmetric distribution always have a skewness of zero? Is a distribution with a skewness of zero always symmetric?
- What are some ways to measure (from data that is provided) the dependency that may exist between processes?
- What are the main types of correlation coefficients and how are they calculated from a given data set?
- What would happen to the measured Pearson correlation coefficient between two data sets if in one of the data sets: a) each of the values is doubled? b) each of the values has a constant amount added to it?
- Assuming that the values in each of two data sets are all different to each other, what would happen to the measured Spearman correlation coefficient if very small changes are made to any of the values?
- How does the slope of the (least-squares) linear regression relate to the correlation coefficient between the data sets?

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