lecture2 - Review of Probability Theory CWR 6536 Stochastic...

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Review of Probability Theory CWR 6536 Stochastic Subsurface Hydrololgy
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Random Variable (r.v.) A variable (x) which takes on values at random, and may be thought of as a function of the outcomes of some random experiment. The r.v. maps sample space of experiment onto the real line The probability with which different values are taken by the r.v. is defined by the cumulative distribution function, F(x), or the probability density function, f(x).
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Examples Discontinuous r.v. - die tossing experiment
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Examples Categorical r.v. – An observation, s( α ), that can take on any of a finite number of mutually exclusive, exhaustive states (s k ) , e.g. soil type, land use, landscape position An indicator random variable can be defined The frequency of occurrence of a state f (s k ) can be determined as the arithmetic average of n indicator data (i( α ,s k ) )where: The joint frequency of two states s k and v k is ( 29 = = n k k s i n s f 1 , 1 ) ( α ( 29 otherwise 0 ) s( if 1 , = = = k k s s i ( 29 ( 29 k v i n k s i n k v k s f , 1 , 1 ) , ( = =
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lecture2 - Review of Probability Theory CWR 6536 Stochastic...

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