Random Experiments and Uncertainty

A random experiment is a process that produces an outcome, where the exact result cannot be predicted in advance, even if the process is repeated under identical conditions.

The key idea is not ignorance. The key idea is inherent uncertainty.

Examples include:

• Rolling a die
• Selecting a student at random
• Measuring the lifetime of a device

Statistics begins by accepting that some systems do not behave deterministically.

What Makes an Experiment Random

An experiment is random if:

• The outcome is known to belong to a well-defined set
• The specific outcome cannot be predicted with certainty
• Repetition under identical conditions does not remove uncertainty

Randomness is a property of the process, not the observer.

The Sample Space

The sample space is the complete collection of all possible outcomes of a random experiment.

It must satisfy two conditions:

• Every possible outcome is included