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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 […]