## FANDOM

228 Pages

Wiki page for the Theory of Probability (STATS 116) class in summer 2012.

## SyllabusEdit

The material covered in the course was guided by Sheldon Ross's textbook, A First Course in Probability. Chapters 1-6 were covered in detail, and portions of chapters 7-8 were discussed in the last few weeks of the course. These chapters cover basic combinatorics, axioms of probability, conditional probability, random variables (discrete and continuous), joint distributions, expected value, and limit theorems.

## Material on final examEdit

Professor Siegmund emphasized the importance of a conceptual understanding of the material covered over specific distributions and solutions. However, he gave an outline of the distributions students should be familiar with on the last day of class and the important concepts.

### Distributions that may be on the examEdit

1. Binomial
2. Normal
3. Poisson
4. Geometric
5. Negative Binomial
6. Hypergeometric
7. Multinomial
8. perhaps Beta
9. Bivariate Normal

### Important concepts/formulasEdit

1. $\operatorname{E}(\sum_i c X_i) = \sum_i c \operatorname{E}(x)$
2. $\operatorname{Var}(\sum_i c X_i) = \sum_i \operatorname{Var}(c X_i) + 2 \sum\sum_{i < j} c_i c_j \operatorname{Cov}(X_i,X_j)$
• the $2 \sum_{i \neq j} c_i c_j \operatorname{Cov}(X_i,X_j)$ term drops out when the X's are independent random variables
3. $\operatorname{E}(X) = \operatorname{E}( \operatorname{E}( X\mid Y))$, also known as the Wikipedia:Law of total expectation
4. $\operatorname{Var}(X) = \operatorname{Var}(\operatorname{E}(X | Y)) + \operatorname{E}(\operatorname{Var}(X|Y))$. known as the Wikipedia:law of total variance
5. moment-generating functions and generating functions
6. joint density functions
7. limit theorems (law of large numbers and central limit theorem)