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 7th 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.

- Population, Sample and Processes
- 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
- Point Estimation
- Statistical Intervals
- Test of Hypotheses
- Simple Linear Regression (time permitting)

See the webpage of the spring 2010 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:

- (1.1) 3, 7
- (1.2) 17, 19, 25, 27
- (1.3) 35, 39, 41
- (1.4) 45, 49, 51, 59

Material covered:

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

Exercises (the numbers in square brackets refer to the 6th edition of the textbook):

- (2.1) 3, 5, 9
- (2.2) 13, 17, 21
- (2.3) 32, 36, 40

Fisrt HW due on Wednesday 7 September

**Third week**

Material covered:

- 2.4 (Conditional Probability)
- 2.5 (Indipendence)

- (2.4) 50, 58, 63
- (2.5) 80 [78], 84 [82], 87 [85]

**Fourth week**

Material covered:

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

- (3.1) 6, 8, 10
- (3.2) 12, 16, 19 [20], 23 [22], 27 [26]
- (3.3) 29 [28], 35 [34], 37 [36], 38 [37], 42 [41]
- (3.4) 48 [46], 54 [50], 58 [54], 63 [59], 65 [61]

**Fifth week**

Material covered:

- 3.5 (Hypergeometric Distribution)
- 3.6 (The Poisson Probability Distribution)
- 4.1 (Continuous Random Variables and Probability Density Functions)
- 4.2 (Cumulative Distribution Functions and Expected Values)

Exercises:

- (3.5) 69, 70, 72
- (3.6) 85, 88, 89, 92
- (4.1) 2, 5, 8
- (4.2) 11, 17, 22, 25

**Sixth week**

Material covered:

- 4.3 (The Normal Distribution)
- 4.4 (The Exponential Distribution)

Exercises:

- (4.3) 28, 29, 31, 35, 41, 46
- (4.4) 59, 69

The first midterm will be on October 5th.

Preparation material for the first midterm:

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

Third HW due on Wednesday 12 October

Seventh 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, 12, 15, 17
- (5.2) 22, 25, 27, 30
- (5.5) 58, 59, 64, 68, 73

Eigth week

Material covered:

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

- (4.6) 87, 88
- (5.3) 37, 40, 41, 42
- (5.4) 46, 49, 51, 53, 56

Fourth HW due on Wednesday 2 November

The second midterm will be on Monday 11/7. It will cover all the material up to Chapter 6 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.

Nineth week

Material covered:

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

- (6.1) 1, 5, 7, 11, 19
- (6.2) 22, 23, 25, 30

Tenth week

Material covered:

- 12.1 (The Simple Linear Regression Model)
- 12.2 (Estimating Model Parameter)

- (12.1) 3, 7, 9
- (12.2) 12, 16, 21, 24

Fifth HW due on Wednesday 30 November

Tenth week

Material covered:

- 7.1 (Basic Properties of Confidence Intervals)

- (6.2) 20, 22, 23, 25, 29, 30
- (7.1) 1, 2, 4, 5, 8, 11

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, 4, 5, 8, 11
- (7.2) 12, 15, 18, 24, 26
- (7.3) 28, 29, 32, 38

Twelfth week

Material covered:

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

- (8.1) 3, 5, 8, 11
- (8.2) 15, 19, 23, 25, 26
- (8.4) 46, 54, 56

Solution set for the midterms: midterm 1 and midterm 2

Preparation material for the final. Here is a link to collected previous term exams with some solutions.