### Office Hours: MW 2-3, Skiles 224. Grader Office Hours: T 1-2 and W 12-1, Skiles 137.

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.

#### Arguments covered.

• 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 fall 2005 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, 53, 59

Second week

Material covered:

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

Exercises:

• (2.1) 3, 5, 9
• (2.2) 13, 17, 21
• (2.3) 32, 35, 40

First HW due Wednesday January 25

Third week

Material covered:

• 2.4 (Conditional Probability)
• 2.5 (Indipendence)
• 3.1 (Random Variables)
• 3.2 (Probability Distributions for Discrete Random Variables)
Exercises:

• (2.4) 50, 58, 63
• (2.5) 78, 82, 85 [83]
• (3.1) 6, 8, 10
• (3.2) 12, 16, 20, 22, 26

Fourth week

Material covered:

• 3.3 (Expected Values of Discrete Random Variable)
• 3.4 (The Binomial Probability Distribution)
• 3.5 (Hypergeometric Distribution)
Exercises:

• (3.3) 28, 34, 36, 37, 41
• (3.4) 46, 50, 54 [52], 59 [57], 61 [59]
• (3.5) 65 [63], 66 [64], 68 [66]

Second HW due Monday February 13

Fifth week

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)
• 4.4 after pag. 177 (The Exponential Distributio)

Exercises:

• (3.6) 81 [79], 84 [82], 88 [86]
• (4.1) 1, 5, 8
• (4.2) 11, 18, 22, 25
• (4.4) 59 [58], 61 [60], 63 [62]

Sixth week

• 4.3 (The Normal Distribution)
• 4.6 (Probability Plots)
• Review for the midterm

Exercises:

• (4.3) 26, 27, 30, 33, 37, 42, 51 [49]
• (4.6) 81 [79], 83 [81], 91 [87]
First midterm Monday February 20

Seventh week

• 5.1 (Jointly Distributed Random Variables)

Exercises:

• (5.1) 1, 3, 8, 12, 15, 17, 20

Eighth week

• 5.2 (Expected Values,Covariance and Correlation)
• 5.3 (Statistics and their distribution)
• 5.5 (The Distribution of a Linear Combination)
Exercises:

• (5.2) 22, 25, 27, 30, 36
• (5.3) 37, 40, 41, 42
• (5.5) 58, 59, 64, 65, 68, 69, 73

Nineth week

• 5.4 (The Distribution of the Sample Mean)
• 6.1 (Some General Concepts of Point Estimation)
• 6.2 (Methods of Point Estimation)
Exercises:

• (5.4) 46, 48, 51, 53, 55, 56
• (6.1) 1, 3, 5, 7, 11, 14, 19
• (6.2) 20, 22, 23, 25, 29, 30
Solution set for HW from chapter 5 and 6

Tenth week

Review for the test

Eleventh week

Material covered:

• 7.1 (Basic Properties of Confidence Intervals)
• 7.2 (Large Sample Confidence Interval for the Population Mean and Proportion)
Exercises:

• (7.1) 1, 2, 4, 5, 8, 11
• (7.2) 12, 15, 18, 24, 26

Due to the low average I will curve the second midterm by adding 25 points to all results. Since there where several very low score you can try to solve this take home retake for the second midterm. Download it here in pdf or html format. The test has to be completed individually. No collaboration is allowed. In case I will dectect collaboration, the tests of the involved persons will be considered void. By downloading it you agree to this rule. The due date is Friday April 21.

Solution set for the reatke test.

Twelveth week

Material covered:

• 8.1 (Hypotheses and Test Procedures)
• 8.2 (Tests about a Population Mean)
Exercises:

• (8.1) 3, 5, 8, 11
• (8.2) 15, 19, 23, 25, 26
Final Preparation Material

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.