Event (probability Theory) - A Note On Notation

A Note On Notation

Even though events are subsets of some sample space Ω, they are often written as propositional formulas involving random variables. For example, if X is a real-valued random variable defined on the sample space Ω, the event

can be written more conveniently as, simply,

This is especially common in formulas for a probability, such as

The set u < X ≤ v is an example of an inverse image under the mapping X because if and only if .