Probability theory: Difference between revisions

Revision as of 18:48, 18 January 2023

Revision as of 20:40, 18 January 2023

Line 21:

===Motivation===

Consider an [[Experiment (probability theory)|experiment]] that can produce a number of outcomes. The set of all outcomes is called the ''[[sample space]]'' of the experiment. The ''[[power set]]'' of the sample space (or equivalently, the event space) is formed by considering all different collections of possible results. For example, rolling an honest dicedie produces one of six possible results. One collection of possible results corresponds to getting an odd number. Thus, the subset {1,3,5} is an element of the power set of the sample space of die rolls. These collections are called ''events''. In this case, {1,3,5} is the event that the die falls on some odd number. If the results that actually occur fall in a given event, that event is said to have occurred.

Probability is a [[Function (mathematics)|way of assigning]] every "event" a value between zero and one, with the requirement that the event made up of all possible results (in our example, the event {1,2,3,4,5,6}) be assigned a value of one. To qualify as a [[probability distribution]], the assignment of values must satisfy the requirement that if you look at a collection of mutually exclusive events (events that contain no common results, e.g., the events {1,6}, {3}, and {2,4} are all mutually exclusive), the probability that any of these events occurs is given by the sum of the probabilities of the events.<ref>{{cite book |last=Ross |first=Sheldon |title=A First Course in Probability |publisher=Pearson Prentice Hall |edition=8th |year=2010 |isbn=978-0-13-603313-4 |pages=26–27 |url=https://books.google.com/books?id=Bc1FAQAAIAAJ&pg=PA26 |access-date=2016-02-28 }}</ref>