### Grader Office Hours: T 1-2.

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, 7th or 6th ed., 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 7th and 6th editions of the book I will indicate in square brackets the number relative to the 6th edition.

The final grade will be based on the following rules: 45% final, 35% midterms, 20% 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 2010 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 (the numbers in square brackets refer to the 6th edition of the textbook):

• (2.1) 3, 5, 9
• (2.2) 13, 17, 21
• (2.3) 32, 36 [35], 40

Third week

Material covered:

• 2.4 (Conditional Probability)
• 2.5 (Indipendence)
• 3.1 (Random Variables)
• 3.2 (Probability Distributions for Discrete Random Variables)
Exercises (the numbers in square brackets refer to the 6th edition of the textbook):

• (2.4) 50, 58, 63
• (2.5) 80 [78], 84 [82], 87 [85]
• (3.1) 6, 8, 10
• (3.2) 12, 16, 19 [20], 23 [22], 27 [26]

Second HW due on September 21th.

The first midterm will be on September 23th.

Preparation material for the first midterm:

Fourth week

Material covered:

• 3.3 (Expected Values of Discrete Random Variable)
• 3.4 (The Binomial Probability Distribution)
• 3.5 (Hypergeometric and Negative Binomial Distribution)
• 3.6 (The Poisson Probability Distribution)
Exercises:
• (3.3) 29 [28], 35 [34], 37 [36], 38 [37], 42 [41]
• (3.4) 48 [46], 54 [50], 58 [54], 63 [59], 65 [61]
• (3.5) 69 [65], 70 [66], 72 [68], 75 [71], 78 [74]
• (3.6) 85 [81], 88 [84], 89 [85], 92 [88]

Fifth week

Material covered:

• 4.1 (Continuous Random Variables and Probability Density Functions)
• 4.2 (Cumulative Distribution Functions and Expected Values)

Exercises:

• (4.1) 1, 5, 8
• (4.2) 11, 17 [18], 22, 25

Solution set for the first midterm.

Sixth week

Material covered:

• 4.3 (The Normal Distribution)
• 4.4 (The Exponential Distribution)
• 5.1 (Jointly Distributed Random Variables)

Exercises:

• (4.3) 28 [26], 29 [27], 32 [30], 35 [33], 41 [37], 46 [42]
• (4.4) 59, 69 [63]
• (5.1) 1, 8, 12, 15, 17

Seventh week

Material covered:

• 5.2 (Expected Values,Covariance and Correlation)
• 5.4 (The Distribution of the Sample Mean)
• 5.5 (The Distribution of a Linear Combination)

Exercises:

• (5.2) 22, 25, 27, 30
• (5.4) 46, 48, 51, 53, 56
• (5.5) 58, 59, 64, 68, 73

Fourth HW due on November 2nd.

The second midterm will be on November 4th.

Preparation material for the second midterm:

Solution set for the second midterm.

Eighth week

Review for Midterm and Midterm

Nineth week

Material covered:

• 5.3 (Statistics and their distribution)
• 6.1 (Some General Concepts of Point Estimation)

Exercises:

• (5.3) 37, 40, 41, 42
• (6.1) 1, 3, 5, 7, 11, 14, 19

Here is the makeup test for the second midterm. It is optional. It is due Thursday December 2.

Tenth week

Material covered:

• 6.1 (Methods of Point Estimation)
• 7.1 (Basic Properties of Confidence Intervals)
Exercises:

• (6.2)  20, 22, 23, 25, 29, 30
• (7.1) 1, 2, 4, 5, 8, 11

Eleventh week

Material covered:

• 7.2 (Large Sample Confidence Interval for the Population Mean and Proportion)
• 8.1 (Hypotheses and Test Procedures)
• 8.2 (Tests about a Population Mean)
Exercises:

• (7.2) 12, 15, 18, 24, 26
• (8.1) 3, 5, 8, 11
• (8.2) 15, 19, 23, 25, 26

Preparation material for the final. Here is a link to collected previous term exams with some solutions.