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 three midterms the first of which will be on Wednesday February 4th.

The exercises listed are only suggested. The more you do the better it is. In case of differences between the two books I will indicate in square brackets the number relative to the 5th edition.

**First week**

Material covered: section 2.1 (Sample Spaces and Events), 2.2 (Axioms, Interpretations, and Properties of Probabilities), and 2.3 (Counting Techniques).

Suggested exercises: (2.1) 3,5,9, (2.2) 13, 17, 21 (2.3) 32, 35, 40

**Second week**

Material covered: section 2.4 (Conditional Probability), 2.5 (Independence), 3.1 (Random Variable)

Suggested exercises: (2.4) 50, 58, 63 (2.5) 78, 82, 85 [83] (Supplementary Exercises) 97, 104, 111 (3.1) 2, 7, 9.

**Third week**

Material covered: section 3.2 (Probability Distribution for a Discrete Random Variable), 3.3 (Expected Values of a Discrete Random Variable)

Suggested exercises: (3.2) 13, 22, 25 (3.3) 28, 29

**Fourth week**

Material covered: 3.3 (Expected Values of a Discrete Random Variable, cont.), 3.4 (The Binomial Probability Distribution), 3.5 (Hypergeometric and Negative Binomial Distributions),

Suggested exercises: (3.2) 37, 40, 43, (3.4) 52, 54, 62, (3.5) 66, 67 (3.6)

**Fifth week**

Material covered: 3.6 (The Poisson Probability Distribution)

Suggested exercises: (3.6) 83, 85

**Sixth week**

Material covered: 4.1 (Continuous Random Variable and Probability Distributions) 4.2 (Cumulative Distribution Functions and Expected Values) 4.3 (The Normal Distribution)

Suggested exercises: (4.1) 3, 5, 9 (4.2) 11, 15, 21 (4.3) 29, 31, 39, 47 [45]

**Seventh week**

Material covered: 4.4 (The Gamma Distribution and Its Relatives) 5.1 Jointly Distributed Random Variables) 5.2 (Expected Values, Covariance and Correlation)

Suggested exercises: (4.3) 33, 41, 45, 49, 53 (4.4) 59, 61, 63 (5.1) 1, 9, 15 (5.2) 23, 27, 35

**Eighth 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) 5.3 (Statistics and Their Dstribution) 5.4 (Distribution of the Sample Mean)

Suggested exercises: (1.1) 3, 7 (1.2) 13, 17, 25, 27 (1.3) 35, 39, 41, (1.4) 45, 49, 53, 59, (5.3) 37, 41, 43 (5.4) 49, 51, 53, 56

**Nineth week**

Material covered: 6.1 (Some General Concepts of Point Estimation) 6.2 (Methods of Point Estimation [the subsection "The Method of Moments" was not covered])

Suggested exercises: (6.1) 1, 5, 7, 11, 17 (6.2) 25, 26, 29, 33, 37

**Tenth week**

Material covered: 7.1 (Basic Properties of Confidence Intervals) 7.2 (Large Sample Confidence Intervals for a Population Mean and Proportion)

Suggested exercises: (7.1) 3, 5, 9, 11 (7.2) 13, 17, 23, 25

February 4: Midterm. Practice test and solution. The test will cover up to the Hypergeometric Distribution. A review class where I'll solve the practice test is tentatively scheduled for Monday 3 form 5:00pm to 6:00pm pending availability of a classroom. The practice test contains the kind of question you may find in the midterm but is not meant as a guideline for the midterm.

** The second midterm will be on March 3.** Note the change of date due to
the high number of people that will be out of town on March 5.

The test will cover sec. 3.6, 4.1, 4.2, 4.3, 5.1, 5.2. The property of linear functions and sums of Normal variable will be used.

Practice test and solutions.

** The third midterm will be on April 14.**

Practice test and solutions.

** The makeup final is fixed for Tuesday April 27 at 11. We meet in my office.
Only people with a good reason. **

Here are few practice exercises for the final with solutions. I'll add the solutions and more exercises tomorrow. I I'll keep upgrading this page so I suggest you to check it.