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A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability distribution is known as probability mass function.
In situation 2, option 2a has a 10% chance of losing $500 and a 90% chance of losing $0, and option 2b has a 5% chance of losing $1000 and a 95% chance of losing $0. This circumstance can be described with the expected utility equations below: Situation 1 Option a: U(-$500) Option b: 0.5 U(-$1000) + 0.5 U($0) Situation 2
The 'discrete case' given above is the special case arising when X takes on only countably many values and μ is a probability measure. In fact, the discrete case (although without the restriction to probability measures) is the first step in proving the general measure-theoretic formulation, as the general version follows therefrom by an ...
In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probability of successes (random draws for which the object drawn has a specified feature) in draws, without replacement, from a finite population of size that contains exactly objects with that feature, wherein each draw is either a success or a failure.
These are also the three discrete distributions among the six members of the natural exponential family with quadratic variance functions (NEF–QVF). More general distributions can be defined by fixing some initial values of p j and applying the recursion to define subsequent values. This can be of use in fitting distributions to empirical data.
In probability theory and statistics, a categorical distribution (also called a generalized Bernoulli distribution, multinoulli distribution [1]) is a discrete probability distribution that describes the possible results of a random variable that can take on one of K possible categories, with the probability of each category separately specified.
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