Review of Probability and Statistics

MSAN 504 - Review of Probability and Statistics

Instructor: Jeff Hamrick

Course Syllabus

Summer 2013

SUMMARY INFORMATION

Instructor: Jeff Hamrick, Ph.D., CFA, FRM

Office: Masonic 211

Office Hours: Half an hour before and after class.

Cell Phone: 617/943-4619

Email Address: jhamrick@usfca.edu

Class Location: 101 Howard Street, Room 451

Class Time: 10:00 a.m. - 12:00 noon on Thursdays and Fridays


ON COURSE OBJECTIVES. Any student who successfully completes this boot camp should:

  • Understand the definitions of probability mass functions, probability density functions, and cumulative distributions functions, as well as moments and cumulants;
  • Know the properties of the most famous examples of random variables (Bernoulli, binomial, exponential, Poisson, normal, etc.);
  • Master the underpinnings of the two most common parameter estimation techniques, maximum likelihood estimation and the method of moments;
  • Understand the difference between a sample and a population;
  • Be able to state the Central Limit Theorem, understand its importance, and apply it in a variety of basic situations;
  • Be able to implement, by hand and in R, all elementary one- and two-sample tests of hypotheses and confidence interval constructions (means, proportions, correlation, ratios of variances, etc.);
  • Understand the fundamental axioms, rules, and laws of probability theory;
  • Simulate (using R) random numbers governed by various probability distributions using the method of inverse transformation and the acceptance-rejection technique;
  • Be able to use R to generate standard numerical and visual summaries of data, including the five-number summary, box-and-whiskers plots, histograms, kernel density histograms, scatter plots, and stem-and-leaf plots;
  • Define, and work with examples related to, conditional probability;
  • Understand the importance of the concept of independence;
  • Prove and use the Law of Total Probability;
  • Use the Law of Total Probability to prove Bayes' Theorem and be able deploy Bayes' Theorem in a variety of practical situations;
  • Understand the difference between, for example, a Bayesian estimator and a traditional point estimator;
  • Work with random vectors as well as random variables;
  • Be able to state, and explain, the assumptions that drive the standard univariate linear regression model; and
  • Be able to generate point estimates for the coefficients in the standard univariate linear regression model by solving the normal equation.