What is "bernoulli distribution"

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kurtosis =$\frac{1-6pq}{pq}$|
entropy = − qln(q) − pln(p) |
mgf =q + pe |
char =q + pe |
pgf =q + pz |
fisher = $\frac{1}{p(1-p)}$|

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In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist Jacob Bernoulli, is the probability distribution of a random variable which takes the value 1 with success probability of p and the value 0 with failure probability of q = 1 − p. It can be used to represent a coin toss where 1 and 0 would represent "head" and "tail" (or vice versa), respectively. In particular, unfair coins would have p ≠ 0.5.

The Bernoulli distribution is a special case of the two-point distribution, for which the two possible outcomes need not be 0 and 1. It is also a special case of the binomial distribution; the Bernoulli distribution is a binomial distribution where n=1.