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

This preview shows pages 1–5. Sign up to view the full content.

Review of Probability Theory CWR 6536 Stochastic Subsurface Hydrololgy

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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).
Examples Discontinuous r.v. - die tossing experiment

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 ) , ( = =
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 03/27/2012 for the course CWR 6536 taught by Professor Graham during the Spring '11 term at University of Florida.

### Page1 / 18

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online