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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]
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
The probability mass function of this distribution, over possible outcomes k, is (;) = {=, = = [3] This can also be expressed as ... The Likelihood Function for a ...
Binomial probability mass function and normal probability density function approximation for n = 6 and p = 0.5. If n is large enough, then the skew of the distribution is not too great. In this case a reasonable approximation to B(n, p) is given by the normal distribution (, ()),
Besides the probability function, the cumulative distribution function, the probability mass function and the probability density function, the moment generating function and the characteristic function also serve to identify a probability distribution, as they uniquely determine an underlying cumulative distribution function. [10]
In probability theory and statistics, the Poisson distribution (/ ˈ p w ɑː s ɒ n /) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. [1]
An alternative parameterization of the distribution gives the probability mass function (=) = () where = and =. [ 1 ] : 208–209 An example of a geometric distribution arises from rolling a six-sided die until a "1" appears.
The probability mass function (pmf) for the mass fraction of chains of length is: () = (). In this equation, k is the number of monomers in the chain, [1] and 0<a<1 is an empirically determined constant related to the fraction of unreacted monomer remaining. [2]
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