| Probability Theory • Introduction to Probability Theory and Forms of Data Presentation - Contingency Tables • Review of Basic Set Theory • Definition of Events in terms of sets • Complementary and Mutually Exclusive Events. • Interpretation of Probability in terms of relative frequencies. • Axioms of Probability Theory • Addition Formula for probability • Conditional Probability • Bayes Theorem and Law of Total Probability • Concept of Independent Events • Network Problems and Determination of Reliability of Networks • Counting Techniques and Application to Sample Spaces with large numbers of sample points • Discrete Random Variables and the Probability mass function • Special Discrete Probability Distributions – Binomial, Poisson Distribution • Application of Poisson distribution to engineering problems - Queuing Theory • Expected Value and Variance, Chebychev's Inequality • Continuous Random Variables (Probability Density Function and Cumulative Distribution Function) • Properties of a probability density, expected value and variance. • The Gaussian (Normal) distribution and its properties and importance in application. • The exponential distribution and its relation to the Poisson process and queuing theory • The Gamma distribution and the Weibull Distribution and their application to modelling times to failure
Statistics • Introduction to Statistics – Inference and Estimation of Parameters. • The central limit theorem. • Large/Small Sample confidence interval estimates for the population mean and the T-distribution. • Large Sample confidence interval estimates for a population proportion. • Introduction to hypothesis testing and the idea behind the process. • Hypothesis testing on a population mean (large and small samples). • Hypothesis testing on a population proportion (large sample). • Categorical Data: Chi-squared goodness of fit test. Chi-squared independence test. • Simple Linear Regression. Correlation/Causation. Prediction Intervals. Hypothesis testing. • Discussion of relation of studied material to simple engineering experiment design. |