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)
Famous quotes containing the word note:
“However intense my experience, I am conscious of the presence and criticism of a part of me, which, as it were, is not a part of me, but a spectator, sharing no experience, but taking note of it, and that is no more I than it is you. When the play, it may be the tragedy, of life is over, the spectator goes his way. It was a kind of fiction, a work of the imagination only, so far as he was concerned.”
—Henry David Thoreau (1817–1862)