Hassett and Stewart's "Probability for Risk Management"

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A set of notes on Hassett and Stewart, 2009. Other texts. The syllabus.

Syllabus

• Chapter 1. Probability: a tool for risk management. pp. 1–7

  Who uses probability; an example from insurance; probability and statistics; some history; computing technology.

• Chapter 2. Counting for probability. pp. 7–45

  What is probability? The language; notation; set identities; counting.

• Chapter 3. Elements of probability. pp. 45–83

  Counting equally-likely and not-equally-likely outcomes; conditional probabilities; independence; Bayes's Theorem.

• Chapter 4. Discrete random variables. pp. 83–113

  Random variables; their probability functions; central tendencies and expected values; variance and standard deviation; population and sample statistics.

• Chapter 5. Commonly used discrete distributions. pp113–149

  Binomial, hypergeometric, Poisson, geometric, negative-binomial distributions.

• Chapter 6. Applications for discrete random variables. pp 149–175.

  Sections 6.1, 6.2.1 only: Functions of random variables and their expectations; moments of a random variable.

• Chapter 7. Continuous random variables. pp. 175–195

  Defining continuous random variables; mode, median, and percentiles; mean and variance.

• Chapter 8. Commonly-used continuous distributions. pp. 195–255

  Uniform, exponential, gamma, normal, log-normal, beta distributions; fitting theoretical distributions to real problems.

  excluding 8.6, 8.7, Pareto and Weibull

• Chapter 9. Applications for continuous random variables. pp. 255–287

  Expected values; mixed distributions.

  excluding 9.2, 9.3, 9.4, 9.6

• Chapter 10. Multivariate distributions. pp. 287–321.

  Joint distributions for discrete variables; conditional distributions (discrete); independence (discrete). Multinomial distribution.

  excluding 10.2, 10.3.2, 10.3.3 continuous, 10.4.2

• Chapter 11. Applying multivariate distributions. pp. 321–373

  Distributions of functions of two random variables; expected values; sums of more than two variables; double expectation theorems; compound Poisson distribution.

  excluding 11.1.4 11.2.3 continuous, 11.2.5 continuous, 11.2.8, 11.3