Astronomy 505

Probability

Intuition - Judgement based on intuition; a combination of rational statistics , personal observations, and superstition.
- Easily biased by non-rational use of data.
Classic Theory - Calculation of the ratio of favourable to total outcomes. Does not involve experiment. Computed by counting N_E events of of N total possible events, where all outcomes are equally likely.
- All outcomes must be equally likely.
- Cannot handle an infinite number of possible outcomes.
Frequency of Ocurrence - Perform an experiment n times, testing for the occurence of event E.
- We must estimate from a finite number of trials.
- We postulate that n_E/n approaches a limit as n goes to infinity.
Axiomatic Theory - Define a random experiment H (with nondeterministic outcomes), a sample description space (the set of all outcomes), and an event (a subset of the sample description space which satisfies certain constraints).
Consider the following definitions of axiomatic theory: