### Office Hours: MW 1:00 - 2:00, 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 9th ed., Thomson

The syllabus can be found here. You can see how the class will develop on the webpage of the previous time I teached it.

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 is tentatively scheduled for Wednesday February 21 and the second on Wednesday March 28.

#### 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 Spring 2016 class for previous tests and material.

First week-Third 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)
• 2.2 (Axioms, Interpretations and Properties of Probabilities)

Exercises:

• (1.3) 34, 38
• (1.4) 49, 51
• (2.1) 3, 5, 9
• (2.2) 13, 21

First HW due on January 29.

Fourth 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

Fifth week

Material covered:

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

Exercises:

• (3.1) 6, 10
• (3.2) 16, 23
• (3.3) 29, 35, 42

Second HW due on February 12

Sixth week

Material covered:

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

Exercises:

• (3.4) 49, 54 63
• (3.5) 70, 72
• (3.6) 85, 89

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
• (4.2) 11, 25
• (4.3) 28, 29, 31, 41
• (4.4) 59, 69
Third HW due on February 26.

The first midterm will be on February 28. The midterm will cover the material up to section 4.4.

Preparation material for the first midterm:

Solution set for the first midterm.

Nineth week

Material covered:

• 4.6 (Probability Plots)
• 5.1 (Jointly Distributed Random Variables)
• 5.2 (Expected Values,Covariance and Correlation)

Exercises

• (4.6) 88
• (5.1) 1, 8, 15, 17
• (5.2) 22, 25, 30

Tenth week

Material covered:

• 5.5 (The Distribution of a Linear Combination)
• 5.3 (Statistics and their distribution)
• 5.4 (The Distribution of the Sample Mean)
Exercises:
• (5.3) 37, 41, 42
• (5.4) 48, 49, 53, 56
• (5.5) 59, 64, 68

Forth HW due on April 2.

The second midterm will be on Wednesday April 4. 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:

Solution set for the second Midterm.

Here is the text of the Optional Makeup for the second Midterm. Check it out and let me know if you have question. It is due Monday April 23 before class. You can submit it at the beginning of Monday class, via email or by sliding it under my office door. Your submission must contain the first page signed

Solution set for the take home Midterm.

The exercise listed below are intended to help your preparation toward the final. They will not be collected.

Eleventhth week

Material covered:

• 6.1 (Some General Concepts of Point Estimation)
• 6.2 (Methods of Point Estimation)
Exercises:
• (6.1) 1, 5
• (6.2) 22, 23, 25

Twelveth 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)
Exercises:
• (7.1) 1, 2, 8
• (7.2) 12, 16, 24
• (7.3) 30, 32

Therteenth week

Material covered:

• 8.1 (Hypotheses and Test Procedures)
• 8.2 (Tests about a Population Mean)
Exercises:
• (8.1) 2, 14
• (8.2) 15, 23, 25
Preparation material for the final. Here is a link to collected previous term exams with some solutions.