MA 222 - Probability & Statistics
Introduces the essentials of probability theory and elementary statistics. Lectures and assignments greatly stress the manifold applications of probability and statistics to computer science, production management, quality control, and reliability. A statistical computer package is used throughout the course for teaching and for assignments. Contents include: descriptive statistics, pictorial and tabular methods, and measures of location and of variability; sample space and events, probability axioms, and counting techniques; conditional probability and independence, and Bayes' formula; discrete random variables, distribution functions and moments, and binomial and Poisson distributions; continuous random variables, densities and moments, normal, gamma, and exponential and Weibull distributions unions; distribution of the sum and average of random samples; the Central Limit Theorem; confidence intervals for the mean and the variance; hypothesis testing and p-values, and applications for the mean; simple linear regression, and estimation of and inference about the parameters; and correlation and prediction in a regression model.
Prerequisites: MA 116
A student completing this class is expected to understand probability reasoning. In addition he/she would have a good understanding of working with probability and have rudimentary notions of statistics. For an in-depth understanding of statistics the MA331 continues this class.
- Demonstrate an understanding of basic principles of probability, and sample spaces.
- Demonstrate understanding of conditional probability, independence and Bayes rule.
- Know the basic discrete distributions (Binomial, Geometric, Negative Binomial, Hypergeometric, and Poisson) and how to work with them.
- Know the basic continuous distributions (Uniform, Normal, Student t, Gamma and Beta) and know how to work with them
- Understand how to calculate fundamental concepts such as the cumulative distribution function, expectations, and distributions for functions of random variables.
- Know how to work with bivariate distributions and how to calculate basic two-variable statistics (covariance, correlation).
- Know the definition and be able to calculate the Characteristic function of a distribution; know how to apply the Central Limit Theorem.
- Know how to describe distributions using graphs and numerical descriptors.
- Understand basic methods of point estimation.
- Be able to evaluate estimators, construct confidence intervals, and perform hypothesis tests in the context of a single population sample.
Devore, Jay L., Probability and Statistics for Engineering and the Sciences, seventh edition, Duxbury, 2007
Ghahramani, Saeed, Fundamentals of Probability with Stochastic Processes, third edition, Prentice Hall, 2004