Unit 6: Probability Essentials
|Main Concepts | Demonstration | Teaching Tips | Data Analysis & Activity | Practice Questions | Connections | Fathom Tutorial | Milestone|
Main ConceptsWe'll study Probability in 3 units. The appetizer is a short unit on the basics: rules, terminology and the basic calculus of probability. The main course is a longer unit on random variables, expectations and variance. For dessert we'll talk about (and do) simulations.
• Probability in this course represents the relative frequency of outcomes after a great many (infinitely many) repetitions.
• We study probability because it is the tool that lets us make an inference from a sample to a population. Probability is thus a means to an end, but is not an end in itself.
• Probability is used to understand what patterns in nature are "real" and which are due to chance. In Statistics we frequently ask, is this a typical occurrence or an unusual occurrence?
• Independence is the fundamental concept of probability and statistics.
• Conditional probability is also of fundamental importance, in part because it helps us understand independence.