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 .
Read more about this topic: Event (probability Theory)
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“The most considerable difference I note among men is not in their readiness to fall into error, but in their readiness to acknowledge these inevitable lapses.”
—Thomas Henry Huxley (1825–95)