Probability Essentials

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 Main Concepts

We'll study Probability in 3 units. The appetizer is a short unit on the basics: rules, terminology, the basic calculus of probability. The main course is a longer unit on random variables, expectations, 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 occurence?

• Independence is the fundamental concept of probability and statistics.

• Conditional probability is also of fundamental importance, in part because it helps us understand independence.