Random Phenomena & Random Variables

Random Phenomena
A random phenomenon is one whose individual occurrences yield random results, but display a regular distribution after many repetitions.

For example: When you toss a coin once, the result is random, but when you toss a coin many times, the proportion of tosses resulting in heads will be about equal to the proportion resulting in tails.

The more outcomes are observed, the more closely the results will follow set proportions.

Random Variables
A random variable is a variable whose individual values are determined by a random phenomenon.
Random variables are usually symbolised by capital letters from near the alphabet.

The mean of a sample chosen randomly from a population (e.g. an SRS) is a random variable.