Chapter 1 STAT 203: Introduction to Probability Theory

This chapter contains past exam problems of STAT 203: Introduction to Probability Theory. For this class, there are two textbooks used for this class, DeGroot and Schervish (2012) and Casella and Berger (2002). A possible syllabus is listed here.

• Sample space, sigma algebra, and the definition of probability.

• Counting methods. Combinatorial methods. Multinomial coefficients.

• Probability of a union of events. Conditional probability and independent events. Bayes theorem.

• Probability density function, probability mass function, cumulative distribution function, and quantile function.

• Bivariate distributions and multivariate distributions.

• Conditional distributions and marginal distributions.

• Functions of a single random variable. Functions of two or more random variables. Probability integral transformation.

• Expectation and variance. Moments and moment generating functions. Covariance and correlation.

• Conditional arguments: conditional expectation, conditional variance, and condition distributions.

• Discrete random variables and their distribution properties. Examples: uniform, Bernoulli, binomial, multinomial, Poisson, hypergeometric, and negative binomial distributions.

• Continuous random variables and their distribution properties. Examples: uniform, normal, beta, gamma, and exponential distributions.

References

Casella, George, and Roger Berger. 2002. Statistical Inference. 2nd ed. Belmont, CA: Duxbury Resource Center.

DeGroot, Morris, and Mark Schervish. 2012. Probability and Statistics. 4th ed. Boston, MA: Addison Wesley.