Define each of the following.


d. Sample space

Verified step by step guidance

1. Understand that the term 'sample space' is a fundamental concept in probability theory and statistics.
2. Recognize that the sample space represents the set of all possible outcomes of a random experiment or trial.
3. Express the sample space mathematically as \(\Omega\) or \(S\), where \(\Omega = \{\text{all possible outcomes}\}\).
4. Note that each outcome in the sample space is mutually exclusive and collectively exhaustive, meaning no two outcomes can happen simultaneously and all possible outcomes are included.
5. For example, if the experiment is tossing a fair coin once, the sample space is \(\Omega = \{\text{Heads}, \text{Tails}\}\).

Key Concepts

Sample Space

The sample space is the set of all possible outcomes of a random experiment. It represents every result that can occur, ensuring a complete description of the experiment's possibilities. For example, in a coin toss, the sample space is {Heads, Tails}.

Random Experiment

A random experiment is a process or action that leads to one of several possible outcomes, where the result cannot be predicted with certainty beforehand. Understanding this helps in defining the sample space accurately.

Outcome

An outcome is a single possible result of a random experiment. Each outcome is an element of the sample space, and collectively, all outcomes form the complete sample space.