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Probability distributions – Probability distributions

📘 Notes

The Discrete Random Variable (AS Statistics)

A random variable is a variable whose value is determined by chance.

1. Discrete Random Variables

A discrete random variable can take only certain values and these values occur randomly.

Examples include:

Number of heads when tossing a coin several times
Number of defective items in a sample
Number of goals scored in a football match

2. Probability Distribution

A probability distribution lists all possible values of a discrete random variable and the probability of each value.

\(x\)	0	1	2	3
\(P(X=x)\)	0.1	0.4	0.3	0.2

The probabilities must satisfy:

3. Properties of a Probability Distribution

Each probability satisfies \(0 \le p \le 1\).
The sum of all probabilities equals 1.
The variable can only take the listed values.