Random Variable

A random variable is a calculated value which depends on the results of an experiment.

A random variable is mapped with a function from the Sample Space to it’s value.

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Example: Sampling

$\mathbb{S}=\{(1,1),(1,2),(2,1),(2,2)\}$

$Y$ is a random variable equal to the sum of the tuple values contained in the Sample Space.

Individual examples of $Y$: $Y((2,1))=3$ $Y((2,2))=4$

The set of outputs for which $Y$ is a value: $\{Y=3\}=\{(1,2),(2,1)\}$ $\{Y=1\}=\varnothing$

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Example: Real World Random Variables

• Number of defective items in a batch
• Number of cars crossing a bridge daily
• Highest weekly temperatures in Dublin
• Trading price of a gold bullion each day