Probability Basics for Machine Learning
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Description: # Measure Theory Measure theory is one of the most important analysis in theoretical probability. But what is measure theory? Why is it so important to theoretical probability? How does it work? Where can measure theory be applied? These are common questions that would ring your brain and the objective of this notebook is not only to try and answer the above questions, but also to convince and build an interest in continuing learning about measure theory. ### What is a Measure?

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Description: # Theory of Probability <br/> ## Probability Spaces

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Description: # Mutually Exclusive Events ## What are mutually exclusive events?

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Description: # Independent Events Consider the example of drawing a ball from a bucket consisting of many different colored balls. For simplicity, consider that there are only two different colored balls - 6 Green balls and 4 Red balls, 10 balls in total. Now draws can be made in two different ways: * with replacement - The ball drawn in every single draw is kept back into the bucket, keeping the total number of balls and mixture of colored balls constant, from draw to draw.
Description: # Discrete Distributions or Probability Mass Functions (PMFs) Probability distribution is a function that generates the probabilities of occurrence of all possible outcomes in an experiment. Consider an experiement of rolling of the die. If the random variable X is used to denote the outcome of the die roll, then the probability distribution of X would take the value $\frac{1}{6}$ for $X \to \{1, 2, 3, 4, 5, 6\}$.