MAT 301 — Probability and Math Stats I
This course emphasizes the calculus-based probability theory necessary for the study of statistical inference. Topics include pictorial and tabular results of descriptive statistics, an introduction to probability theory, independence, and conditional probabilities including Bayes’ Theorem. Several discrete (binomial, hypergeometric, negative binomial, Poisson) and continuous (Normal, exponential, gamma, uniform) probability distributions will be studied including the concepts of a distribution function, probability mass, and density functions, expected value, variance, and standard deviation. Joint probability distributions and sampling distributions follow. We shall see how the law of large numbers and the Central Limit Theorem are used in statistics. The course will then apply the concepts of probability learned to the point estimates, confidence intervals, tests of hypothesis, and regression. Probability can be taught as a branch of mathematics but is much better appreciated if taught Students will use computer software such as Maple/R. In fact, learning how to use Maple/R is among major course objectives.