Here are the topics from MTH311 that we will review along with the section number in the new book. This will more of less cover the things learned in chapters 1-4 in Pitman’s Probability book.

• Random Variables Discrete and Continous random variables. These are different but really quite similar. The important topics are:

  • The state space $\Omega$, an outcome $\omega$ and an event $A$. (1.2)

  • Distribution of $X$ (2.1, 2.2, 5.1, 5.2,5.7)

  • Examples of random variables: random sampling, uniform, Bernoulli. (1.5, 4.1, 5.2)

  • $E(g(x))$, $E(g(X_1,\dots,X_n))$ (3.1,3.2,3.3,3.4,3.5,5.4,5.5,5.9)

  • Independence, exchangeability (2.5,2.6)

• Basics of Probability

  • Conditioning, Bayes Rule (2.3,2.4,5.11)

  • Mean, standard deviation, covariance, median: (3.1,3.2,3.3,3.4,3.5,5.4,5.5,5.9,)

• More examples of probability

  • The uniform distribution

  • The Bernoulli distribtion, Binomial, Hypergeometric, negative binomial. (4.1,4.2,4.3,4.4)

  • The Normal distribution, normal approximation to the binomial. (6.1,,4.5,4.7)

  • Central limit theorem and the law of large numbers. (4.5,4.7)

  • The geometric, exponential and Poisson distribtions. (4.4,6.2,4.6)

  • The $\chi^2$ distribution. (6.4)

Wow, that sounds like a whole semesters worth! Well, actually we aren’t going to go into great detail except where it is needed (and you’ll let me know). Some things that are new are exhangeablity, some things on conditioning, and the $\chi^2$ distribution.