Probability and Statistics is a course that equips you with the necessary tools for making wise decisions in the face of uncertainty.

In section 1, you will learn the difference between a population and a sample, as well as the difference between descriptive and inferential statistics. In this chapter we focus on descriptive statistics and the various methods we can use to organize and display data that we collect from a sample in an attempt to draw conclusions about the whole population. You will learn how to organize the data into frequency and relative frequency distribution tables, and how to use these tables to display the data on bar graphs, histograms, pie charts, and boxplots. Moreover, you will learn how to calculate measures of center and measures of variability that statisticians use as sample representatives.

In section 2, we recall important definitions from set theory that we will use extensively for counting and probability. We learn the meaning of probability, sample space, events and relationships between events. We also learn how to use Venn Diagrams and Tree Diagrams to simplify problems. Finally, we learn the concept of independence of events as well as conditional probability.

In section 3, we learn the various techniques we can use to count the number of elements in a given set. We learn the multiplication rule for counting, the use of factorials, permutations and combinations. We also learn an extra bunch of problem-specific counting techniques such as permutations involving fixing positions and/or fixing order.

In section 4, we define a random variable and its two types (discrete and continuous). We also define probability mass functions, cumulative distribution functions, expected value and variance. Furthermore, We dig deeper into discrete random variables and their distributions: Bernoulli distribution, Binomial distribution, Hypergeometric distribution, geometric distribution, negative binomial distribution, and Poisson distribution.