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Combinatorics
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
Binomial coefficients are usually presented in a triangular array, called Pascal’s Triangle (although it certainly predates Pascal; see [2] or [4], which specify earlier Chinese, Indian, and European sources). In the figure below, the entry in row n and column k is (nk).
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Published in Jamal T. Manassah, Elementary Mathematical and Computational Tools For Electrical and Computer Engineers Using Matlab®, 2017
where Ckn is the binomial coefficient and represents the number of combinations of n objects taken k at a time without regard to order. It is equal to n!/k!(n — k)!. All these combinations are equally probable.
Probability Distributions
Published in Alan R. Jones, Probability, Statistics and Other Frightening Stuff, 2018
The Binomial Distribution is a discrete probability distribution that calculates the probability of getting a number of successes from a number of independent events where each event has the same chance (i.e. probability) of success. We can liken it to a set of switches that are either on or off.
Partial sums of analytic functions defined by binomial distribution and negative binomial distribution
Published in Applied Mathematics in Science and Engineering, 2022
Rubab Nawaz, Saira Zainab, Fairouz Tchier, Qin Xin, Afis Saliu, Sarfraz Nawaz Malik
One of the most essential discrete probability distributions is Binomial distribution. When there are two possible outcomes, then Binomial distribution model is used which is an important probability model. In a Bernoulli trial, the random experiment has two hypothetical results that are success or failure. If the number of trials m = 1, then it is called Bernoulli distribution that is special case for the Binomial distribution. Binomial distribution determines the probability of successful outcomes. It has two parameters, m and p where m denotes the number of trial and p denotes the success outcomes.
An incomplete taxonomy of Bayesian models with examples from industrial statistics applications
Published in Quality Engineering, 2020
For a simple discrete model, consider y the number of successes in n Bernoulli trials with probability of success p, i.e., y has a Binomial(n,p) distribution. Then the pmf takes the familiar form: