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.

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Course Team

Instructor Professor Deepa Kundur

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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, 9^th 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)

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