Initial commit

Author: maximumGain

LICENSE.md

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+MIT License
+
+Copyright (c) [2020] [Fan Zhou]
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

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+# basic-probability
+Matlab source code for basic probability used in information theory.
+Static methods are defined in a class named 'probabilityTool'. 
+Simply call a function in this class by probabilityTool.<functionname>.
+All methods provides default input for computation.   
+Your inputs are collected using <varargin>.
+
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+Example:
+Jointly distributed random variables X and Y are defined with a joint probability distribution pXY(x,y) = Pr(X = x, Y = y).
+Then the marginal distribution pX(x) and pY(y) can be computed by:
+[px,py] = probabilityTool.marginalize(pxy)          %pxy is the joint probability distribution pXY(x,y)
+or
+[px,py] = probabilityTool.marginalize(pxy,'r')       which returns rational number.
+
+The program also provides default values, invoking 
+[px,py] = probabilityTool.marginalize
+
+
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+Type methods(probabilityTool) to see all methods in this class.
+
+The software provides the following functions.
+-   Theorem of total probability                                       @probabilityTool.PRy   
+-   Marginalization                                                           @probabilityTool.marginalize 
+-   Compute joint distribution                                         @probabilityTool.computeJointDistribution
+-   Compute "all-related" probability                              @probabilityTool.computeAllP
+-   Bayes rule                                                                  @probabilityTool.bayes
+-   Compute expected value                                           @probabilityTool.computeExpection
+-   Expected value of a function                                     @probabilityTool.expectionOfaFunction 
+-   Compute variance                                                     @probabilityTool.computeVariance
+-   An example of binary random vector                        @probabilityTool.binaryRandomVectorExample (uses @binomialPR)
+-   Use Chebyshev inequality on random vectors          @largeNumberExperiment (uses @randomSamples)
+
+
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+
+Notations in source code:
+-   px:         Pr(X = x)
+-   py:         Pr(Y = y)
+-   pxy:       Pr(X=x,Y=y) joint probability
+-   pxgy:     Pr(X=x | Y=y) conditional probability
+-   pygx:     Pr(Y=y | X=x) conditional probability
+-   EX:        E[X] expection of pX(x)
+-   EgX:      E[g(x)] expection of a function g(x), where g(x) is a function of pX(x)
+-   Var:       Var[X] variance of pX(x)
+
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
+
+
+
+
+v1.0    June 29, 2020    Initial release