### **
Department of Statistics**

University of California

Berkeley, California

Fall Semester, 2002

#### **
Statistics 134, Section 2**

Concepts of Probability

Units: 3

#### Instructor: Antar Bandyopadhyay

Office Hours: 357 Evans, MF 11:00 - 12:00

email: `antar@stat.berkeley.edu`

#### ** Course Outline**

- Mathematical set-up for probability, equally likely outcomes, basic counting arguments, conditional probability, Bayes' rule, independent events.
- Sampling with and without replacement, Binomial distribution, Normal and Poisson approximations.
- Discrete random variables, Binomial, Poisson, Hypergeometric, Geometric distributions, expectation, variance, generating functions.
- Discrete joint distributions, independent variables, repeated trials.
- Law of Large Numbers, Central Limit Theorem.
- Continuous random variables, density, cumulative distribution function, change of variable, expectation, variance.
- Uniform, Exponential, Gamma, Normal distribution.
- Poisson process.
- Continuous joint distribution, independence.
- Discrete and continuous conditional distributions and conditional expectations.
- Bivariate Normal distribution.

#### ** Prerequisites**

Calculus ( Math - 53 or equivalent )

#### ** Texts**

Probability by Jim Pitman.

#### ** Grading**

- Homework : 30%
- Midterm : 30%
- Final : 40%