# ECE 286: Probability and Statistics

A course in probability and statistics for Engineering Science students focusing on building solid probabilistic and statistical foundations. Topics include: sample space, events, definitions of probability, conditional probability, Bayes’ theorem, important classes of discrete and continuous random variables and their distributions, joint, conditional, and marginal distributions, expectation, moment generating and characteristic functions, transformations of random variables, central limit theorem and approximations. Graphical methods, quantile plots, point and interval estimation of population parameters, method of maximum likelihood. Hypotheses testing, simple and multiple regression, correlation analysis, and introduction to Bayesian statistics.

### Course Team

#### Instructor

• Professor Deepa Kundur

### Course Syllabus

This course makes use of the following text:

R.E. Walpole, R.H. Myers, S.L. Myers and K. Ye, Probability & Statistics for Engineers & Scientists, 9th ed., Pearson, Inc., 2011. ISBN-13 978-0-13-411585-6.

The following topics and text book sections are covered in this course:

• Introduction to Statistics, Data Analysis and Probability: The role of probability, sampling procedures, measures of location, measures of variability, discrete and continuous data, statistical modelling and graphical methods, sample space, events, definitions of probability, conditional probability, Bayes’ rule. (Text, §1.1-1.6, §2.1, 2.2, 2.4-2.7)
• Random Variables, Probability Distributions and Expectation: Concept of a random variable, discrete probability distributions, continuous probability distributions, joint probability distributions, mean, variance, covariance, linear combinations of random variables. (Text, §3.1-3.4, §4.1-4.3)
• Discrete and Continuous Probability Distributions: Discrete uniform, binomial and multinomial, hypergeometric, negative binomial, geometric, Poisson, continuous uniform, normal distribution and its applications, normal, gamma, exponential, chi-squared, Weibull.  (Text, §5.1-5.5, §6.1-6.7, 6.10)
• Functions of Random Variables: Transformations of random variables, moments and moment generating functions. (Text, §7.1-7.3)
• Fundamental Sampling Distributions and Data Descriptions: random sampling, central limit theorem, sampling distributions, t-distribution, F-distribution, quantiles, quartiles and percentiles. (Text, portions of §8.1-8.8)
• Estimation Problems: statistical inference, unbiased estimator, variance of a point estimator, interval estimation, mean estimation, standard error of a point estimate, prediction intervals, tolerance limits, absolute error and relative error, sample-size calculation, single- and two-sample estimators, maximum likelihood estimation.  (Text, portions of §9.1-9.14)

### Lecture Notes and Related Handouts

Notice: The following materials have been made public to help has study aids for those taking the course and the general public. They are not intended under any circumstance to be placed on repository sites for use by third-party distributors for profit or even not-for-profit reasons. If you would like to make the content known to others, please link to it.

### Problem Sets and Solutions

All the problem set questions are posted ahead of time for your convenience in case you want to study ahead. At any point in the course, it is only expected however that you have covered the problem sets corresponding to the sections completed in class (as bolded above).
Please note: DQ.X = “Drill Problem Q.X from the text” and Q.X=”Problem Q.X from the text”.

 Problem Set Relevant Text Sections Problem Set Questions Solutions 1 1.1 – 1.6, 2.1, 2.2, 2.4 1.1, 1.5, 1.6, 1.7, 1.11, 1.12, 1.16, 1.18, 1.19, 2.1, 2.3, 2.5, 2.9, 2.14, 2.16, 2.17 PDF (by Wei Cui) 2 2.5-2.7 2.51, 2.55, 2.58, 2.61, 2.67, 2.73, 2.85, 2.93, 2.94, 2.105, 2.110, 2.113, 2.127 PDF (by Wei Cui) 3 3.1-3.4 3.1, 3.3, 3.5(a), 3.8, 3.9, 3.11, 3.13, 3.14, 3.15, 3.16, 3.29, 3.36, 3.38, 3.40, 3.56, 3.57 PDF (by Wei Cui) 4 4.1-4.3 4.6, 4.7, 4.12, 4.17, 4.18, 4.21, 4.23, 4.35, 4.41, 4.50, 4.58, 4.60, 4.65, 4.66 PDF (by Wei Cui) 5 5.1-5.5 5.4, 5.7, 5.11, 5.15, 5.29, 5.31, 5.33, 5.49, 5.50, 5.54, 5.56, 5.61, 5.66, 5.94 PDF (by Danny Zhang) 6 6.1-6.7, 6.10 6.1, 6.4, 6.5, 6.7, 6.9, 6.13, 6.22, 6.24, 6.27, 6.33, 6.36. 6.41, 6.44, 6.47 PDF (by Danny Zhang) 7 8.1-8.5 8.1, 8.14, 8.17, 8.20, 8.32, 8.33, 8.35, 8.36, 8.40, 8.41 PDF (by Susanne Pyda) 8 8.6-8.8 8.44, 8.47, 8.51, 8.59, 8.69; Optional: 8.43. PDF (by Susanne Pyda) 9 9.1-9.4 9.1, 9.2, 9.6, 9.9 PDF (by Shaurya Gupta)

Note: Problem set solutions are courtesy of Wei Cui, Danny Zhang, Susanne Pyda and Shaurya Gupta.