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 9th 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 9th and 8th editions of the book I will indicate in square brackets the number relative to the 8th edition.

The final grade will be based on the following rules: 45% final, 40% midterms,15% HW. Curving will be done on the final result.

The first midterm will be on- 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 Fall 2011 class for previous tests and material.

**First week**

Material covered:

- 1.1 (Population, Sample and Processes)
- 1.2 (Pictorial and Tabular methods in Descriptive Statistics)
- 1.3 (Measure of Location)
- 1.4 (Measure of Variability)

Exercises:

- (1.3) 34, 38
- (1.4) 49, 51

**First HW** due on **January 25**.

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

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

**Fourth week**

Material covered:

- 3.1 (Random Variables)
- 3.2 (Probability Distributions for Discrete Random Variables)
- 3.3 (Expected Values of Discrete Random Variable)

- (3.1) 6, 8, 10
- (3.2) 16, 23, 27

- (3.3) 29, 35 39, 42

Material covered:

- 3.4 (The Binomial Probability Distribution)
- 3.5 (Hypergeometric Distribution)
- 3.6 (The Poisson Probability Distribution)

Exercises:

- (3.4) 49, 54 63, 65

- (3.5) 70, 72
- (3.6) 85, 89, 92

The first midterm will be on February 17. The midterm will cover the material up to section 3.6.

Preparation material for the first midterm:

- Test and solution set.
- Test and solution set.
- Test and solution set.
- Test and solution set

**Sixth and seventh weeks**

Material covered:

- 4.1 (Continuous Random Variables and Probability Density Functions)
- 4.2 (Cumulative Distribution Functions and Expected Values)
- 4.3 (The Normal Distribution)
- 4.4 (The Exponential Distribution)

Exercises:

- (4.1) 2, 5, 8
- (4.2) 11, 17, 25
- (4.3) 28, 29, 31, 41

- (4.4) 59, 69

Fourth HW due on March 7.

Eighth week

Material covered:

- 5.1 (Jointly Distributed Random Variables)
- 5.2 (Expected Values,Covariance and Correlation)
- 5.5 (The Distribution of a Linear Combination)

Exercises:

- (5.1) 1, 8, 15, 17
- (5.2) 22, 25, 30
- (5.5) 59, 64, 68

Nineth week

Material covered:

- 5.3 (Statistics and their distribution)
- 5.4 (The Distribution of the Sample Mean)

- (5.3) 37, 41, 42
- (5.4) 48, 49, 53, 56

The second midterm will be on Wednesday 3/30. It will cover all the material up to Chapter 5 included. You may use a scientific calculator but no laptop or calculator able to do symbolic differentiation or integration. No cheat sheet will be allowed.

Preparation material for the second
midterm:

- Test and solution set.
- Test and solution set.
- Test and solution set.
- Test and solution set.

**Solution set** for the second
Midterm.

**Fifth HW due on** April 4. The exercises are those listed above
for Chapter 5.

Here is the text of the **Otional Makeup**
for the second Midterm. Check it out and let me know if you have
question. It is due **Monday 11 in the evening**. You can submit it
in class, via email or by sliding it under my office door. Your
submission must contain the **first page signed**

**Tenth week**

Material covered:

- 6.1 (Some General Concepts of Point Estimation)
- 6.2 (Methods of Point Estimation)

- (6.1) 1, 5

- (6.2) 22, 23, 25

**Eleventh week**

Material covered:

- 7.1 (Basic Properties of Confidence Intervals)
- 7.2 (Large Sample Confidence Interval for the Population Mean and Proportion)
- 7.3 (Interval Based on a Normal Population Distribution)

- (7.1) 1, 2, 8

- (7.2) 12, 16, 24

- (7.3) 30, 32

**Fifth HW due on Monday 25 April**

**Twelfth week**

Material covered:

- 8.1 (Hypotheses and Test Procedures)
- 8.2 (Tests about a Population Mean)

- (8.1) 2, 4, 14
- (8.2) 15, 19, 23, 25