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STATS 2B03 (25)
Chapter 3

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McMaster University
Aaron Childs

Stats 2B03: Statistical Methods for Science Chapter 3: Some Basic Probability Concepts 3.2 Two Views of Probability: Objective and Subjective - Concept of objective probability may be categorized further under the headings of classical probability and the relative frequency concept of probability - Classical probability: if an event can occur in N mutually exclusive and equally likely ways, and if m of these possess a trait E, the probability of the occurrence of E is equal to m/N - Relative frequency probability: if some process is repeated a large number of times, n, and if some resulting event with the characteristic E occurs m times, the relative frequency of occurrence of E, m/n, will be approximately equal to the probability of E - Subjective probability: measures the confidence that a particular individual has in the truth of a particular proposition - Bayesian methods: example of subjective probability, since it takes into consideration the degree of belief that one has in the chance that an event will occur  Prior probability: probability based on prior knowledge, prior experience, or prior results derived from prior data collection activity  Posterior probability: probability obtained by using new information to update or revise a prior probability 3.3 Elementary Properties of Probability - Axiomatic approach to probability:  Given some process with n mutually exclusive outcomes E , E ,…E , 1 2 n the probability of any event E is aisigned a nonnegative number. That is, P(E)i0. Two events are mutually exclusive if they cannot occur simultaneously  Sum of the probabilities of the mutually exclusive outcomes is equal to 1. P(E 1+P(E )+2+P(E )=1. nroperty of exhaustiveness and refers to the fact that the observer of a probab
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