### MATH 3670 Probability and Statistics with Applications

### Spring 2015

### TTr 12:05-1:35, Van Leer W200

### Office Hours: TTr 2:30-3:30, Skiles 133B

The course will introduce the basic notion of probability theory and
its application to statistics. The focus will be on the discussion of
applications.

The text that will be used is:

Jay L. Devore, **Probability and Statistics**,
8th or 8th ed., Thomson

The syllabus can be found here.

There will be two midterm.

The exercise listed are for HW collection. I will collect them
every
two weeks and grade 2 or 3 exercises among the one assigned. In case of
differences between the 8th and 7th editions of the book I will
indicate in square brackets the number relative to the 7th edition.

The final grade will be based on the following rules: 45%
final, 35%
midterms, 20% HW. Curving will be done on the final result.

#### Arguments covered.

- Axioms, Interpretations and Properties of Probabilities
- Probability Distributions for Discrete Random Variables
- Example of Discrete Random Variables
- Continuous Random Variables and Probability Density
Functions
- Example of Continuous Random Variables
- The central limit theorem
- Jointly Distributed Random Variables
- Population, Sample and Processes
- Point Estimation
- Statistical Intervals
- Test of Hypotheses
- Simple Linear Regression (time permitting)

See the webpage
of the sSummer 2013 class for previous tests and material.

**First week**

Material covered:

- 2.1 (Sample Spaces and Events)
- 2.2 (Axioms, Interpretations and Properties of Probabilities)

Exercises:

- (2.1) 3, 5, 9
- (2.2) 13, 21

**Second week**
Material covered:

- 2.3 (Counting Technique)
- 2.4 (Conditional Probability)
- 2.5 (Indipendence)

Exercises:

- (2.3) 32, 40
- (2.4) 50, 58, 63
- (2.5) 80, 87

**Third week**
Material covered:

- 2.3 (Counting Technique)
- 2.4 (Conditional Probability)
- 2.5 (Indipendence)

Exercises:

- (2.3) 32, 40
- (2.4) 50, 58, 63
- (2.5) 80, 87

**First HW** due on Thursday 22.