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**, Thomson

The syllabus can be found here.

There will be two midterm the first of which will be on Monday September 20th.

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 6th and 5th editions of the book I will indicate in square brackets the number relative to the 5th edition.

The final greade will be based on the following rules: 50% final, 40% midterms, 10% HW. Curving will be done on the final result.

**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)
- 2.1 (Sample Spaces and Events)

Exercises:

- (1.1) 3, 7
- (1.2) 17, 19, 25, 27
- (1.3) 35, 39, 41
- (1.4) 45, 49, 53, 59
- (2.1) 3, 5, 9

**Second week**

Material covered:

- 2.2 (Axioms, Interpretations and Properties of Probabilities)
- 2.3 (Counting Technique)
- 2.4 (Conditional Probability)
- 2.5 (Indipendence)

Exercises:

- (2.2) 13, 17, 21
- (2.3) 32, 35, 40
- (2.4) 50, 58, 63
- (2.5) 78, 82, 85 [83]

**Third week**

Material covered:

- 3.1 (Random Variables)
- 3.2 (Probability Distributions for Discrete Random Variables)

Exercises:

- (3.1) 6, 8, 10
- (3.2) 12, 16, 20, 22, 26

**Fourth week**

Material covered:

- 3.3 (Expected Values od Discrete Random Variable)
- 3.4 (The Binomial Probability Distribution)

Exercises:

- (3.3) 28, 34, 36, 37, 41
- (3.4) 46, 50, 54 [52], 59 [57], 61 [59]

**Fifth week**

Material covered:

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

Exercises:

- (3.5) 65 [63], 66 [64], 68 [66]
- (3.6) 76 [74], 81 [79], 84 [82], 88 [86], 89 [87]

**Test Preparation Material**

Test from previous term: practice test and solution, test and solution.

**Seventh week**

Material covered:

- 4.1 (Continuous Random Variables and Probability Density Functions)
- 4.2 (Cumulative Distribution Functions and Expected Values)

Exercises:

- (4.1) 1, 5, 8
- (4.2) 11, 18, 22, 25

**Eighth week**

Material covered:

- 4.3 (The Normal Distribution)
- 4.4 after pag. 177 (The Exponential Distribution and The Chi-Squared Distribution)

- (4.3) 26, 27, 30, 33, 37, 42, 51 [49]
- (4.4) 59 [58], 61 [60], 63 [62]

**Nineth week**

Material covered:

- 5.1 (Jointly Distributed Random Variables)
- 5.2 (Expected Values,Covariance and Correlation)
- 5.3 (Statistics and their distribution)

- (5.1) 1, 3, 8, 12, 15, 17, 20
- (5.2) 22, 25, 27, 30, 36
- (5.3) 37, 40, 41, 42

**Tenth week**

Material covered:

- 5.4 (The Distribution of the Sample Mean)
- 5.5 (The Distribution of a Linear Combination)
- 6.1 (Some General Concepts of Point Estimation)

- (5.4) 46, 48, 51, 53, 55, 56
- (5.5) 58, 59, 64, 65, 68, 69, 73
- (6.1) 1, 3, 7

**Test Preparation Material**

Test from previous term: practice test and solution, test and solution.

**Eleventh week**

Material covered:

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

- (6.1) 1, 3, 5, 7, 11, 14, 19
- (6.2) 20, 22, 23, 25, 29, 30

**Twelfth 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

Material covered:

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

- (8.1) 3, 5, 8, 11
- (8.2) 15, 19, 23, 25, 26

**Final Preparation Material**

Test from previous term: Test from previous term: practice test and solution, test (NB: exercise 3 contains a typo, can you find it? It is corrected in the solution set) and solution.

Final from previos term:practice final and solution.