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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 28, 2020 Initial release