Practice Problems

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Unit 01 /
Problem 2:


A outcome spaces and events
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Easy


Prove that if an event space has infinitely many events, the outcome space must have infinitely many outcomes.

Solution:

If the number of outcomes is some finite integer $n \in \mathbb{Z}$, then the event space must be the power set or a subset of the powerset. The powerset has size $2^n$, which is finite. Hence, it is not possible to have a finite outcome space but an infinite event space.