Note for COMPLEX VARIABLE and STATISTICAL METHODS - CVSM By JNTU Heroes

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ComplexVariablesandStatistical Methods 1

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Definition of probability • There are two main different definitions of the concept of probability • Frequentist – Probability is the ratio of the number of occurrences of an event to the total number of experiments, in the limit of very large number of repeatable experiments. – Can only be applied to a specific classes of events (repeatable experiments) – Meaningless to state: “probability that the lightest SuSy particle’s mass is less tha 1 TeV” • Bayesian – Probability measures someone’s the degree of belief that something is or will be true: would you bet? – Can be applied to most of unknown events (past, present, future): • “Probability that Velociraptors hunted in groups” • “Probability that S.S.C Naples will win next championship” JNTU World Statistical Methods for Data Analysis 2 2

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Classical probability “The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought. The ratio of this number to that of all the cases possible is the measure of this probability, which is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible.” Pierre Simon Laplace (1749-1827) Pierre-Simon Laplace, A Philosophical Essay on Probabilities JNTU World Statistical Methods for Data Analysis 3 3

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Classical Probability Number of favorable cases Probability = Number of total cases • • Assumes all accessible cases are equally probable This analysis is rigorously valid on discrete cases only – Problems in continuous cases ( Bertrand’s paradox) P = 1/6 (each dice) P = 1/2 P = 1/4 P = 1/10 JNTU World Statistical Methods for Data Analysis 4 4