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Binomial distribution B(n,p) is used to model or predict success in
n trials with p the probability of success in each
trial. The probability of success is (0,1) - a
boolean outcome. The
probability of failure q is (q = 1 - p). When the number of
trials n = 1 (single trial), it is known as Bernoulli trial. When
this function B(n,p) is used for multiple trials (n > 1), the outcome is known as
Bernoulli distribution.
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The Probability mass function f(k,n,p) for binomial distribution is
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for k = 0,1,2,.... n where
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| is known as the Binomial Coefficient. This formulation can be found
in the works of Indian mathematician Pingala around 750 AD.
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We can consider an example of getting heads in six coins tosses (n = 0,...5). The probability
in this case for each trial is 50/50 or 0.5 for head and 0.5 for tail.
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| p = 0.5 and
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| q = 1 - p = (1 - 0.5) = 0.5
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| The probability mass function f(k,n,p) of |
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| Reference |
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Math Reference
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Factorial Script
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Poisson Distribution
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