Grader Name: Heidi Yang

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**,
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.

- 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)

**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)
- 2.4 (Conditional Probability)
- 2.5 (Indipendence)

Exercises:

- (2.1) 3, 5, 9
- (2.2) 13, 17, 21
- (2.3) 32, 36 [35], 40
- (2.4) 50, 58, 63
- (2.5) 80 [78], 84 [82], 87 [85]

**Third week**

Material covered:

- 3.1 (Random Variables)
- 3.2 (Probability Distributions for Discrete Random Variables)
- 3.3 (Expected Values of Discrete Random Variable)

- (3.1) 6, 8, 10
- (3.2) 12, 16, 19 [20], 23 [22], 27 [26]
- (3.3) 29 [28], 35 [34], 37 [36], 38 [37], 42 [41]

Second HW due on February 9th.

The first midterm will be on February 16th.

**Fourth week**

Material covered:

- 3.4 (The Binomial Probability Distribution)
- 3.5 (Hypergeometric and Negative Binomial Distribution)
- 3.6 (The Poisson Probability Distribution)

- (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]

Preparation material for the first midterm:

- Test and solution set.
- Test and solution set.
- Test and solution set.
- Test and solution set.

**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)

Exercises:

- (4.3) 28 [26], 29 [27], 32 [30], 35 [33], 41 [37], 46 [42], 55 [51]
- (4.4) 59, 61, 69 [63]

Seventh week

Material covered:

- 5.1 (Jointly Distributed Random Variables)
- 5.2 (Expected Values,Covariance and Correlation)
- 5.3 (Statistics and their distribution)

Exercises:

- (5.1) 1, 3, 8, 12, 15, 17, 20
- (5.2) 22, 25, 27, 30, 36
- (5.3) 37, 40, 41, 42

Eighth week

Material covered:

- 5.4 (The Distribution of the Sample Mean)
- 5.5 (The Distribution of a Linear Combination)
- 6.1 (Some General Concepts of Point Estimation)

- (5.4) 46, 48, 51, 53, 55, 56
- (5.5) 58, 59, 64, 65, 68, 69, 73
- (6.1) 1, 3, 5, 7, 11, 14, 19

Fourth HW due on March 16th.

The second midterm will be on March 16th.

Preparation material for the second midterm:

- Test and solution set.
- Test and solution set.
- Test and solution set.
- Test and solution set.

Solution set for the second midterm.

Nineth week

Material covered:

- 6.1 (Methods of Point Estimation)
- 7.1 (Basic Properties of Confidence Intervals)

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

Tenth week

Material covered:

- 7.2 (Large Sample Confidence Interval for the Population Mean and Proportion)
- 7.3 (Interval Based on a Normal Population Distribution)
- 7.4 (Confidence Intervals for the Variance and Standard Deviation of a Normal Population)

- (7.2) 12, 15, 18, 24, 26
- (7.3) 28, 29, 32, 38
- (7.4) 43, 45

Retake test. Since the results of the second midterm where not good I will curve them by multiplying all score by a factor of 1.8. Moreover, this is an optional test for those of you that want to improve their result on the second midterm. The test is due next Thursday at the beginning of calss. You are not supposed to collaborate with other student or to seek external help.

Solution set for the retake test.

**Twelveth week**

Material covered:

- 8.1 (Hypotheses and Test Procedures)
- 8.2 (Tests about a Population Mean)

- (8.1) 3, 5, 8, 11
- (8.2) 15, 19, 23, 25, 26

**Thirteenth week**

Material covered:

- 8.4 (P-values)
- 14.1 (Goodeness of Fit Tests)
- 14.3 (Two-Way Contingency Table)

Exercises:

- (8.4) 46 (45), 54 (52), 56 (54)
- (14.1) 4, 7, 10
- (14.3) 24, 27, 31, 33

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