The mean and standard deviation of linear transforms of one or more random variables- Normal approximation for sums of random variables- The Bernoulli distribution and the geometric distribution-

Section 3.3: Simulations. Setting up and carrying out simulations- Sample problems and examples-

Section 3.4: Random Variables-The mean and variance in terms of outcomes and their probabilities. Interpretation of the mean as a center of gravity-

Example problem using Bayes' Theorem. Restatement of the theorem for multiple outcomes of the dependent variable. Summary of section.

Bayes' Theorem definition and discussion on reversing order of conditionality. Sample problem -

Probabilities for sampling with and without replacement. Independence and conditional probability. Checking for independence and mutual exclusive events.

The complement of an event- Probabilities of events and their complements- Independence- Multiplication rule for independent processes- Section 3.2: Conditional Probability- Probabilities and contingency tables- Marginal and joint probabilities- The definition of conditional probability-

Using the R programming language to enter contingency tables, compute marginals, and compute row and column proportions. Interpreting row and column proportions-Plotting bar charts with two variables - Plotting mosaic and pie charts,

Probability of mutually exclusive or disjoint outcome, Probabilities when events are not disjoint-

Summarizing categorical data (introduction)- Contingency tables and bar graphs- Definition of probability and law of large numbers-

Introduction to R and RStudio. Use of RStudio in the cloud and local installation. The normal distribution and calculations involving it in R.

Cumulative histograms. Z-scores. Quartiles. Box plots. interquartile range. Outlier rule. Computing standard deviation and IQR. Linear transformations and their effects on means and standard deviations. Comparing distributions with back-to-back stem and leaf plots, side-by-side box plots, and hollow histograms. Mapping data.