OS2080 Probability and Statistics I

Fundamentals of probability and statistics useful in military modeling. Topics include probability laws and calculation methods, conditional probability, Bayes' Theorem, discrete and continuous random variables, the binomial, geometric, Poisson, exponential, and normal distributions, expectation, variance, and covariance, confidence intervals, hypothesis testing, and simple linear regression. Emphasis is on understanding uncertainty and developing computational skills for military systems analysis.

Prerequisite

Single variable calculus

Lecture Hours

Lab Hours

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.