Grader: Matt Schuchard

Grader Office Hours: email him for appointment

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:

William C. Navidi, **Statistics for Engineers and Scientists**,
2nd Edition,

The syllabus can be found here.

There will be two midterm the first of which will be on Thursday September 27th.

The exercise listed are for HW collection. I will collect them every two weeks and grade 2 or 3 exercises among the ones assigned.

The final greade will be based on the following rules: 50% final, 40% midterms, 10% 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 Sampling
- 1.2 Summary Statistics
- 1.3 Graphical Summaries

- Exercises
- (1.1) 1, 3, 5
- (1.2) 2, 6, 8, 9, 10, 12, 13
- (1.3) 2, 4, 7, 13, 15, 16

**Second week**

- Material covered
- 2.1 Basic Ideas
- 2.2 Counting Methods
- 2.3 Conditional Probability and Independence

- Exercises
- (2.1) 2, 5, 7, 11, 14, 16, 19
- (2.2) 1, 4, 8, 11, 12
- (2.3) 5, 7, 11, 16, 21, 23, 28

Fisrt HW collection ** Thursday September 3rd**

**Third week**

- Material covered
- 2.4 Random Variables

- Exercises
- (2.4) 3, 7, 10, 14, 18, 25

**Forth week**

- Material covered
- 2.5 Linear Functions of Random Variables
- 2.6 Jointly Distributed Random Variables

- Exercises
- (2.5) 3, 8, 10
- (2.6) 9, 10, 11, 21, 23, 26, 28

Second HW collection ** Thursday September 20th**

**Fifth week**

- Material covered
- 3.1 Mesuarement Error
- 3.2 Linear Conbination of Measurements
- 3.3 Uncertainities for Functions of One Measurement
- 3.4 Uncertainities for Functions of several Measurement
- 4.1 The Bernoulli Distribution
- 4.2 The Binomial Distribution

- Exercises
- (3.1) 5, 6
- (3.2) 8, 13, 19
- (3.3) 7
- (3.4) 1, 6
- (4.1) 2, 6, 7
- (4.2) 3, 6, 14, 16, 21

**Sixth week**

- Material covered
- 4.3 The Poisson Distribution
- 4.4 The Hypergeometric Distribution

- Exercises
- (4.3) 7, 9, 13, 19
- (4.4) 1, 2, 11

Third HW collection ** Thursday October 11th**

**Eighth week**

- Material covered
- 4.5 The Normal Distribution
- 4.7 The Exponential Distribution
- 4.9 Some Principle of Point Estimationm

- Exercises
- (4.5) 2, 3, 14, 21, 26
- (4.7) 2, 6, 10
- (4.8) 6

- Material covered
- 4.10 Probability Plots
- 4.11 The Central Limit Theorem
- 4.12 Simulation

- Exercises
- (4.10) 2
- (4.11) 2, 8, 16, 19

- Material covered
- 5.1 Large Sample Confidence Intervals for a Population Mean
- 5.2 Confidence Interval for Proportion
- 5.3 Small Sample Confidence Intervals for a Population Mean
- 5.4 Confidence Intervals for the Difference Between Two Means

- Exercises
- (5.1) 3, 5, 10, 20, 24
- (5.2) 5
- (5.3) 1
- (5.4) 4, 8

Fourth HW collection ** Thursday November 1st**

**Eleventh week**

- Material covered
- 6.1 Large Sample Test for Population Mean
- 6.2 Drawing Conclusion from the Results of Hypothesie Tests
- 6.3 Tests for Population Proportion
- 6.12 Fixed Level Testing

- Exercises
- (6.1) 1, 6, 9, 13
- (6.2) 3, 5, 10, 14,18
- (6.3) 3, 6
- (6.12) 3, 4

- Material covered
- 6.13 Power
- 6.10 The Chi-Square Test
- 6.4 Small SWample Test for Population Mean
- 6.5 Large Sample Test for the Difference Between Two Means
- 6.8 Tests with Paired Data

- Exercises
- (6.13) 1, 5
- (6.10) 1, 8
- (6.4) 3, 6
- (6.5) 2, 8
- (6.8) 5, 11

**Second Midterm** will be on **Thursday November 15**.

Here is a link to collected previous term exams with some solutions.