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Elementary event

From Wikipedia, the free encyclopedia

In probability theory, an elementary event, also called an atomic event or sample point, is an event which contains only a single outcome in the sample space.[1] Using set theory terminology, an elementary event is a singleton. Elementary events and their corresponding outcomes are often written interchangeably for simplicity, as such an event corresponding to precisely one outcome.

The following are examples of elementary events:

  • All sets where if objects are being counted and the sample space is (the natural numbers).
  • if a coin is tossed twice. where stands for heads and for tails.
  • All sets where is a real number. Here is a random variable with a normal distribution and This example shows that, because the probability of each elementary event is zero, the probabilities assigned to elementary events do not determine a continuous probability distribution.