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: 40% final, 40% midterms,20% 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 Spring 2016 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

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

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

Material covered:

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

Exercises:

- (2.3) 32, 40
- (2.4) 50, 58, 63

Material covered:

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

Exercises:

- (2.5) 80, 87
- (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)

Exercises:

- (3.4) 49, 54 63, 65
- (3.5) 70, 72

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

**Sixth and seventh weeks**

Material covered:

- 3.6 (The Poisson Probability Distribution)
- 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:

- (3.6) 85, 89
- (4.1) 2, 5, 8
- (4.2) 11, 25
- (4.3) 28, 29, 31, 41
- (4.4) 59, 69

**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 Friday 3/31. 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.