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Chapter 3

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McMaster University

Statistics

STATS 2B03

Aaron Childs

Fall

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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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