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Related Concept Videos

Probability Distributions01:32

Probability Distributions

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 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson...
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Poisson Probability Distribution01:09

Poisson Probability Distribution

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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
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Applications of Integration to Probability Density Functions01:27

Applications of Integration to Probability Density Functions

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Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF),...
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Probability Histograms01:17

Probability Histograms

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A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
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Probability in Statistics01:14

Probability in Statistics

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Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
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Binomial Probability Distribution01:15

Binomial Probability Distribution

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A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
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Using Three-color Single-molecule FRET to Study the Correlation of Protein Interactions
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Probability Distributome: A Web Computational Infrastructure for Exploring the Properties, Interrelations, and

Ivo D Dinov1, Kyle Siegrist2, Dennis K Pearl3

  • 1Statistics Online Computational Resource (SOCR), Michigan Institute for Data Science (MIDAS), School of Nursing, University of Michigan, Ann Arbor, MI 48109; SOCR Resource, Department of Statistics, University of California, Los Angeles, Los Angeles, CA 90095; Center for Computational Biology, University of California, Los Angeles, Los Angeles, CA 90095.

Computational Statistics
|May 10, 2016
PubMed
Summary
This summary is machine-generated.

The Distributome is a new open-source infrastructure for discovering and using probability distributions. It aids computational research and enhances STEM education with interactive tools.

Keywords:
DistributomeProbability distributionsapplicationsgraphical user interfaceinferencemodelstransformations

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Area of Science:

  • Computational statistics and probability theory.
  • Development of scientific software and educational technology.

Background:

  • Probability distributions are fundamental to modeling natural processes and physical phenomena.
  • A vast number of distributions exist, but only a subset is commonly used.
  • Existing tools lack comprehensive infrastructure for exploring and applying diverse distributions.

Purpose of the Study:

  • To introduce the Distributome, a novel computational and graphical infrastructure.
  • To facilitate the discovery, exploration, and application of a wide range of probability distributions.
  • To support both computational research and science education.

Main Methods:

  • Development of an extensible, open-source, community-built infrastructure accessible online.
  • Implementation of interfaces for human and machine traversal, search, and navigation of distributions.
  • Integration of tools for distribution modeling, analysis of inter-distribution relations, and computational utilization.

Main Results:

  • The Distributome provides a unified framework for accessing and utilizing common probability distributions.
  • Demonstrated applications in computational research, including simulation, data analysis, and model-fitting.
  • Showcased potential for enhancing STEM education through interactive web applications and improved learning assessments.

Conclusions:

  • The Distributome infrastructure significantly enhances the accessibility and application of probability distributions.
  • It offers valuable resources for advancing computational modeling and enriching STEM education.
  • The open-source and community-driven nature ensures portability, extensibility, and compatibility with modern web standards.