Sample space properties
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Sample space properties

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We create a set that we usually denote by capital omega. That set is called the sample space and is the set of all possible outcomes of our experiment. The elements of that set should have certain properties.
First, the elements should be mutually exclusive. If at the end of the experiment, I tell you that this outcome happened, then it should not be possible that another outcome also happened. At the end of the experiment, there can only be one of the outcomes that has happened.
Secondly, the elements should be collectively exhaustive. Together, all of these elements of the set exhaust all the possibilities.
Finally, the sample space should be at the right granularity. Whenever you put together a model, you need to decide how detailed you want your model to be. And the right level of detail is the one that captures those aspects that are relevant and of interest to you.

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