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Probability-mass-function
A Probability Mass Function (PMF) is a fundamental concept in probability theory that describes the distribution of discrete random variables. It assigns a probability to each possible outcome of a discrete event, ensuring that the sum of all probabilities equals one. For instance, when rolling a fair six-sided die, the PMF indicates that each face (1 through 6) has an equal probability of 1/6. PMFs are essential for understanding the likelihood of specific outcomes in various applications, such as games of chance, statistical analysis, and decision-making processes. They provide a clear framework for quantifying uncertainty in discrete scenarios.
Probability Mass and Density Functions
Probability mass and density functions are used to describe discrete and continuous probability distributions, respectively. This allows us to determine the probability of an observation being…
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Distributions
In the previous chapter we used Bayes’s Theorem to solve a cookie problem; then we solved it again using a Bayes table. In this chapter, at the risk of testing your patience, we will solve it one mor...
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Chapter 6 Probability density functions
The code for this chapter is in density.py . For information about downloading and working with this code, see Section 0.2 . 6.1 PDFs The derivative of a CDF is called a probability density function ,...
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Part 03: Describing Random Outcomes: PMF, CDF, and PDF
In the previous article, we introduced the concept of a random experiment using the example of student marks in a class. Now, we will delve deeper into how we mathematically describe the likelihood of...
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What Is A Probability Density Function?
In the wonderful world of statistics, distributions are an absolutely vital component that sits at the center of a universe of mathematics. Distributions are used to describe data mathematically, and…...
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Probability Theory for Deep Learning
A very quick introduction to Random variables, probability mass/density functions, and special distribution functions.
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Statistical Distributions
A probability distribution is a mathematical function that provides the probabilities of the occurrence of various possible outcomes in an experiment. Probability distributions are used to define…
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Deep Learning Book Series 3.1 to 3.3 Probability Mass and Density Functions
This content is part of a series about Chapter 3 on probability from the Deep Learning Book by Goodfellow, I., Bengio, Y., and Courville, A. (2016). It aims to provide intuitions/drawings/python code…...
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Probability
Probability Links Screenshots License Basic concepts in probability for machine learning. This cheatsheet is a 10-page reference in probability that covers a semester’s worth of introductory probabili...
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Probability
Many machine learning methods are rooted in probability theory. Probabilistic methods in this book include linear regression , Bayesian regression , and generative classifiers . This section covers t...
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What Is A Cumulative Distribution Function?
Back in May, I took a look at a distribution function that belongs to most statistical distributions called the Probability Density Function, or PDF. The PDF is a very important part of statistical…
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Probabilistic Matrix Factorization
In this post we introduce probability matrix factorization from a Bayesian Statistics perspective. We also draw connections between optimization and regularization in posterior inference.
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