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Machine Learning: End-to-End guide for Java developers

You're reading from   Machine Learning: End-to-End guide for Java developers Data Analysis, Machine Learning, and Neural Networks simplified

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Product type Course
Published in Oct 2017
Publisher Packt
ISBN-13 9781788622219
Length 1159 pages
Edition 1st Edition
Languages
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Authors (2):
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Krishna Choppella Krishna Choppella
Author Profile Icon Krishna Choppella
Krishna Choppella
Uday Kamath Uday Kamath
Author Profile Icon Uday Kamath
Uday Kamath
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Toc

Appendix B. Probability

Essential concepts in probability are presented here in brief.

Axioms of probability

Kolmogorov's axioms of probability can be stated in terms of the sample space S of possible events, E1, E2, E3, …En and the real-valued probability P(E) of an event E. The axioms are:

  1. P(E) ≥ 0 for all E ϵ S
  2. P(S) = 1
  3. Axioms of probability

Together, these axioms say that probabilities cannot be negative numbers—impossible events have zero probability—no events outside the sample space are possible as it is the universe of possibilities under consideration, and that the probability of either of two mutually exclusive events occurring is equal to the sum of their individual probabilities.

Bayes' theorem

The probability of an event E conditioned on evidence X is proportional to the prior probability of the event and the likelihood of the evidence given that the event has occurred. This is Bayes' Theorem:

Bayes' theorem

P(X) is the normalizing constant, which is also...

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