maximumgain / basic-probability

The Matlab source code for basic probability used in information theory.

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.

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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

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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)

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v1.0 June 28, 2020 Initial release