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Ioannis Pitas (AUTH)
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This lecture overviews Probability Theory that has many applications in a multitude of scientific and engineering disciplines, notably in Pattern Recognition and Machine Learning. It covers the following topics in detail:
- Probability Space, Bayes theorem.
- One random variable, cumulative probability functions, probability density functions, expectation operators, mean, variance, functions of random variables, normal, uniform, Laplacian distributions.
- Two random variables, joint cumulative probability functions, joint probability density functions, expectation operators, independence, correlation coefficient, functions of two random variables, 2D normal, uniform, Laplacian distributions.
- Multiple Random Variables, random vectors, joint cumulative probability functions, joint probability density functions, expectation operators, independence, correlation matrix, covariance matrix, functions of two random variables, multivariate normal distributions.
Finally, a section is devoted on random number and random vector generation.
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