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Probability Distributions

Bernoulli Trials​

TODO

Binomial Distribution​

Useful for computing number of success in n Bernoulli trials.

p(k)=(nk)pk(1−p)n−kp(k) = {n \choose k} p^k (1-p)^{n-k}

Where pp is the probability of success on a given trial, n is the number of trials, and yy is the number of successes in a given trial. (Boslaugh, Statistics in a Nutshell)

Multinomial Distribution​

A generalization of the binomial distribution for more than two outcomes.

Negative Binomial Distribution​

The number of trials it takes for r successes.

p(x)=(x−1r−1)pr(1−p)x−rp(x) = {x - 1 \choose r - 1} p^r (1-p)^{x-r}

Geometric Distribution​

A special case of the negative binomial distribution for r=1r=1.

g(x;p)=p(1−p)x−1g(x;p) = p (1-p)^{x-1}