Chapter 1: Basic Concepts of Probability

Basic Concepts and Definitions

Observation

Any recording of information, be it numerical or categorical

Statistical Experiment

Any procedure that generates a set of observations

Sample Space

The set of all possible outcomes of a statistical experiment, represented by the symbol $S$.

<aside> 💡 $S=\{1,2,3,4,5,6\}$ for a die toss.

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<aside> 💡 $S=\{\text{even, odd}\}$ for a number

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<aside> 💡 $S=\{(H,H),(H,T),(T,H),(T,T)\}$ for two coin flips. Note that both $(H,T)$ and $(T,H)$ are shown so that each outcome is equally likely, but this does not really matter.

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Sample Points

Every outcome in a sample space

<aside> 💡 $(H,H)$ is a sample point for the above example

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Events

A subset of a sample space

Simple Event

Consists of exactly one outcome or sample point

Compound Event