What is a Binomial Distribution?
The binomial distribution is a probability distribution that summarizes the likelihood that a value will take on one of two independent values under a given set of parameters or assumptions.
This distribution is frequently used in statistics to analyze events with two possible outcomes, such as success or failure, yes or no, heads or tails. It's a common model for representing binary data.
Understanding the Formula
The probability of obtaining exactly k successes in n independent Bernoulli trials is given by:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
where C(n, k) is the combination of n items taken k at a time, and p is the probability of success on any given trial.
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