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Probability Distribution

In probability theory and statistics, aprobability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment. In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events. For instance, if the random variableXis used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 forX= heads, and 0.5 forX= tails(assuming the coin is fair). Examples of random phenomena can include the results of an experiment or survey.

Discrete Probability Distribution​

A discrete probability distribution (applicable to the scenarios where the set of possible outcomes is discrete, such as a coin toss or a roll of dice) can be encoded by a discrete list of the probabilities of the outcomes, known as a probability mass function.

Continuous Probability Distribution​

A continuous probability distribution (applicable to the scenarios where the set of possible outcomes can take on values in a continuous range (e.g. real numbers), such as the temperature on a given day) is typically described by probability density functions (with the probability of any individual outcome actually being 0).

A probability distribution whose sample space is the set of real numbers is called univariate, while a distribution whose sample space is a vector space is called multivariate. A univariate distribution gives the probabilities of a single random variable taking on various alternative values; a multivariate distribution (a joint probability distribution) gives the probabilities of a random vector -- a list of two or more random variables -- taking on various combinations of values. Important and commonly encountered univariate probability distributions include the binomial distribution, the hypergeometric distribution, and the normal distribution. The multivariate normal distribution is a commonly encountered multivariate distribution.

Types of distribution​

  1. Uniform distribution
  2. Normal distribution / Gaussian distribution
  3. Gamma distribution
  4. Exponential distribution
  5. Poisson distribution
  6. Binomial distribution
  7. Bernoulli distribution

https://en.wikipedia.org/wiki/Probability_distribution

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