### Office Hours: MW 15:00-16:00, Skiles 224. Grader Office Hours: TR 10:00-11:00, 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 2004 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)

Exercises:

• (1.1) 3, 7
• (1.2) 17, 19, 25, 27
• (1.3) 35, 39, 41

Second week

Material covered:

• 1.4 (Measure of Variability)
• 2.1 (Sample Spaces and Events)
• 2.2 (Axioms, Interpretations and Properties of Probabilities)

Exercises:

• (1.4) 45, 49, 53, 59
• (2.1) 3, 5, 9
• (2.2) 13, 17, 21

First HW due Wednesday September 7

Third week

Material covered:

• 2.3 (Counting Technique)
• 2.4 (Conditional Probability)
• 2.5 (Indipendence)

Exercises:

• (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 Wednesday September 21

Fifth week

• 3.3 (Expected Values od Discrete Random Variable)
• 3.4 (The Binomial Probability Distribution)

Exercises:

• (3.3) 28, 34, 36, 37, 41
• (3.4) 46, 50, 54 [52], 59 [57], 61 [59]

First midterm will be on Monday 26th September

Sixth week

Material covered:

• 3.5 (Hypergeometric Distribution)
• 3.6 (The Poisson Probability Distribution)
• 4.1 (Continuous Random Variables and Probability Density Functions)

Exercises:

• (3.5) 65 [63], 66 [64], 68 [66]
• (3.6) 76 [74], 81 [79], 84 [82], 88 [86], 89 [87]
• (4.1) 1, 5, 8

Third HW due Wednesday October 13.

Eigth week

Material covered:

• 4.2 (Cumulative Distribution Functions and Expected Values)
• 4.3 (The Normal Distribution)
• 4.4 after pag. 177 (The Exponential Distribution and The Chi-Squared Distribution)
• 5.1 (Jointly Distributed Random Variables)

Exercises:

• (4.2) 11, 18, 22, 25
• (4.3) 26, 27, 30, 33, 37, 42, 51 [49]
• (4.4) 59 [58], 61 [60], 63 [62]
• (5.1) 1, 3, 8, 12, 15, 17, 20

Nineth week

Material covered:

• 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

Fourth HW due on November 2nd. Section collected up to 5.2.

Solution to some of the HW problems: 2, 3 and 4 Second midterm will be on Wednesday November 2nd

Tenth week

Material covered:

• 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

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
Final Preparation Material