The graph of a probability mass function. All the values of this function must be non-negative and sum up to 1.
In probability and statistics, a probability mass function (sometimes called probability function or frequency function[1]) is a function that gives the probability that a discrete random variable is exactly equal to some value.[2] Sometimes it is also known as the discrete probability density function. The probability mass function is often the primary means of defining a discrete probability distribution, and such functions exist for either scalar or multivariate random variables whose domain is discrete.
A probability mass function differs from a probability density function (PDF) in that the latter is associated with continuous rather than discrete random variables. A PDF must be integrated over an interval to yield a probability.[3]
The value of the random variable having the largest probability mass is called the mode.
^7.2 - Probability Mass Functions | STAT 414 - PennState - Eberly College of Science
^Stewart, William J. (2011). Probability, Markov Chains, Queues, and Simulation: The Mathematical Basis of Performance Modeling. Princeton University Press. p. 105. ISBN 978-1-4008-3281-1.
^A modern introduction to probability and statistics : understanding why and how. Dekking, Michel, 1946-. London: Springer. 2005. ISBN 978-1-85233-896-1. OCLC 262680588.{{cite book}}: CS1 maint: others (link)
and 25 Related for: Probability mass function information
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a function whose...
cumulative distribution function, or by a multivariate probability density function together with a multivariate probabilitymassfunction. In the special case...
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution...
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different...
The probability of getting exactly k successes in n independent Bernoulli trials (with the same rate p) is given by the probabilitymassfunction: f (...
Probability measure, a real-valued function on a probability space ProbabilitymassfunctionProbability distribution function (disambiguation) This disambiguation...
included variables. For discrete random variables, the conditional probabilitymassfunction of Y {\displaystyle Y} given X = x {\displaystyle X=x} can be...
To understand the above definition of the probabilitymassfunction, note that the probability for every specific sequence of r successes and k failures...
In probability and statistics, the quantile function outputs the value of a random variable such that its probability is less than or equal to an input...
Probability distribution function may refer to: Cumulative distribution functionProbabilitymassfunctionProbability density functionProbability distribution...
distributions. The term is motivated by the fact that the probabilitymassfunction or probability density function of a sum of independent random variables is the...
If X1,X2,…,Xn are discrete random variables, then the marginal probabilitymassfunction should be p X i ( k ) = ∑ p ( x 1 , x 2 , … , x i − 1 , k , x...
{\displaystyle X} follows the hypergeometric distribution if its probabilitymassfunction (pmf) is given by p X ( k ) = Pr ( X = k ) = ( K k ) ( N − K n...
with parameter λ > 0 , {\displaystyle \lambda >0,} if it has a probabilitymassfunction given by:: 60 f ( k ; λ ) = Pr ( X = k ) = λ k e − λ k ! , {\displaystyle...
done by hand, involves a discrete probability distribution, which is characterized by a probabilitymassfunction. The density of the sum of two independent...
distribution. The reference discusses techniques of evaluating the probabilitymassfunction of the Poisson binomial distribution. The following software implementations...
likelihood function (often simply called the likelihood) is the joint probabilitymass (or probability density) of observed data viewed as a function of the...
proposed by Max Born, in 1926. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum...
unchanged when its probability density function (for continuous probability distribution) or probabilitymassfunction (for discrete random variables) is...
in measure and probability theory. Consider two independent random variables X , Y {\textstyle X,\,Y} with probabilitymassfunctions p X ( x ) {\displaystyle...
0 ) = 1 − q . {\displaystyle \Pr(X=1)=p=1-\Pr(X=0)=1-q.} The probabilitymassfunction f {\displaystyle f} of this distribution, over possible outcomes...
joint probabilitymassfunction or probability density function as f ( x , y ) {\displaystyle f(x,y)} and joint cumulative distribution function as F (...
Global Information