Statistical Sciences 2244A/B Lecture Notes - Lecture 5: Frequentist Probability, Frequency (Statistics)
30 Sep 2016
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A measure of the long-run relative frequency of an event occurring, in identical repeated trials. Make an assumption about the theoretical probabilities. # ways that x can occur / # different simple events. Random outcome: uncertain, but follows a regular distribution in a large number of repetitions. Probability of a random outcome: proportion of times the outcome would occur in a long series of repetitions. # times x has occurred / # times trials was repeated. Note: the relative frequency approach can change every time. Thus we use the law of large numbers. The relative frequency probability of an event tends to approach the actual probability as a procedure is repeated. P(x or y) = p(x)+p(y)-p(x and y) Mutually exclusive (disjoint) events cannot occur at the same time. P(x and y) = p(x) x (y | x) Events are independent if knowing the outcome of one event does not change the probability of the other occurring.
