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en.wikipedia.org/wiki/Binomial_distribution

The binomial distribution is the basis for the popular binomial test of statistical significance. The binomial distribution is frequently used to model the number of successes in a sample of size n drawn with replacement from a population of size N.

binomial random variable: A type of discrete random variable used to count the number of occurrences of an event in a random sample in a binomial experiment. A binomial random variable can only be used to count whether a certain event occurs or does not occur, and cannot be used to measure partial states.

And what I'm going to do is I'm going to define a random variable X as being equal to the number of heads after after ten flips of my coin. Now, what makes this a binomial variable? Well, one of the first conditions that's often given for a binomial variable is that it's made up of a finite number of independent trials.

www.statisticshowto.datasciencecentral.com/random-variable

If you aren’t counting something, then it isn’t a binomial random variable. The number of trials in your experiment must be fixed. For example, “the number of times you roll a die before rolling a 3” is not a binomial random variable, because there is an indefinite number of trials.

newonlinecourses.science.psu.edu/stat800/node/29

Probabilities for binomial random variables . The conditions for being a binomial variable lead to a somewhat complicated formula for finding the probability any specific value occurs (such as the probability you get 20 right when you guess as 20 True-False questions.) We'll use Minitab to find probabilities for binomial random variables.

To calculate a binomial distribution, you will need to (a) plug the correct value into each variable, (b) find the binomial coefficient, and (c) evaluate the binomial probability formula. Here we go!

stattrek.com/statistics/dictionary.aspx?definition=binomial_probability

Definition of binomial probability, from the Stat Trek dictionary of statistical terms and concepts. This statistics glossary includes definitions of all technical terms used on Stat Trek website.

www.dummies.com/.../math/statistics/how-to-identify-a-random-binomial-variable

The most well-known and loved discrete random variable in statistics is the binomial. Binomial means two names and is associated with situations involving two outcomes; for example yes/no, or success/failure (hitting a red light or not, developing a side effect or not). A binomial variable has a binomial distribution. A random variable is binomial if […]

Now, for this case, to think in terms of binomial coefficients, and combinatorics, and all of that, it's much easier to just reason through it, but just so we can think in terms it'll be more useful as we go into higher values for our random variable. This is all buildup for the binomial distribution, so you get a sense of where the name comes ...

en.wikipedia.org/wiki/Binomial_regression

In statistics, binomial regression is a regression analysis technique in which the response (often referred to as Y) has a binomial distribution: it is the number of successes in a series of independent Bernoulli trials, where each trial has probability of success . In binomial regression, the probability of a success is related to explanatory variables: the corresponding concept in ordinary ...

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