Probability via Expectation pp 38-48 | Cite as

# Probability

## Abstract

An event A is something which either occurs or does not occur in a particular case. It often has some kind of verbal description: e.g. ‘I win the game’ or ‘the patient survives’. As we saw in Section 2.3, the formal characterization of the event is as a set of realizations *ω*, i.e. a subset of Ω, also denoted by *A*. This is just the set of realizations for which the event occurs. The probability of the event is defined as *P*(*A*) = *E*[*I*(*A*)], (1) where *I*(*A*, *ω*) is the indicator function of the set *A*; the random variable which takes value 1 or 0 according as the event occurs or not. Thus *P*(*A*) can be seen as the expected proportion of times that *A* occurs.

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