### Office Hours: TR 4.30-5.30, Skiles 224. Grader Name: Matt Schuchard Grader Office Hours: TBA.

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 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, 35% midterms, 15% 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 spring 2006 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

First HW collection Thursday January 18. First week HW due.

Second week

Material covered:

• 2.1 (Sample Spaces and Events)
• 2.2 (Axioms, Interpretations and Properties of Probabilities)
• 2.3 (Counting Technique)
• 2.4 (Conditional Probability)
• 2.5 (Indipendence)

Exercises:

• (2.1) 3, 5, 9
• (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

Second HW due Thursday February 1

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]

First Midterm on Thursday February 15

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

First Midterm text and solutions

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 Distribution)

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

Exercises:

• (4.3) 26, 27, 30, 33, 37, 42, 51 [49]
• (5.1) 1, 3, 8, 12, 15, 17, 20
• (5.2) 22, 25, 27, 30, 36

Seventh week

• 5.3 (Statistics and their distribution)
• 5.5 (The Distribution of a Linear Combination)
• 5.4 (The Distribution of the Sample Mean)
Exercises:

• (5.3) 37, 40, 41, 42
• (5.5) 58, 59, 64, 65, 68, 69, 73
• (5.4) 46, 48, 51, 53, 55, 56

Nineth week

• 6.1 (Some General Concepts of Point Estimation)
• 6.2 (Methods of Point Estimation)
Exercises:

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

Eleventh 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, 4, 5, 8, 11
• (7.2) 12, 15, 18, 24, 26
• (7.3) 28, 29, 32, 38

Second Midterm on Tuesday April 10th Test from previous term: practice test and solution, test and solution. Test and solutions set . Solution set for last year second midterm.

Second Midterm text and solutions

Twelveth week

Material covered:

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

• (8.1) 3, 5, 8, 11
• (8.2) 15, 19, 23, 25, 26
• (8.4) 45, 52, 54
Final Preparation Material

Tests from previous terms:

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