# OS3180 Probability and Statistics for Systems Engineering

This course introduces the systems engineering and analysis student to probability, descriptive statistics, inferential statistics, and regression. The modeling and analysis of the stochastic behavior of systems provides the context for the course. Topical coverage includes the normal, binomial, Poisson, exponential, and lognormal distributions; probabilistic measures of system performance; graphical and numerical data summaries; confidence intervals and hypothesis tests based on one or two samples; regression with one or more predictors; and single factor analysis of variance. The lab portion of the class uses spreadsheets to support the modeling and analyses. The course is delivered in block format.

### Prerequisite

SE1001 or equivalent

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### Course Learning Outcomes

·      Learn basic probability concepts and counting techniques. Compare and contrast probability and statistics. Present counting techniques, permutations, combinations, Venn diagrams and conditional probability, independence, disjoint events, law of total probability and Bayes’ theorem.

·      Use concept of discrete and continuous random variables to discuss probability mass functions, probability density functions, cumulative distribution functions, expected value and variance. Learn about joint and marginal distributions, condition distributions and expectation for jointly distributed random variables, covariance and correlation.

·      Specific distributions discussed are Bernoulli, binomial, multinomial, geometric, Poisson discrete distributions. Continuous distributions discussed are uniform, exponential, gamma, normal, chi-squared, F and t distributions.

·      Discuss sampling distributions, central limit theorem, statistical terminology for location (mean, median, trimmed mean), for variability (variance, standard deviation, range) and categorical data (mode, sample proportions, indicator variables).

·      Use numerical, graphical and tabular summaries to describe data. Find point estimates using method of moments and maximum likelihood.

·      Find standard error for sample data then construct confidence and prediction intervals for population parameters using sample data. Also conduct suitable one- or two-sided hypotheses tests and also paired hypotheses tests and tests for proportions.

·      Effectively use simple and multiple regression to create models for data.