Binomial and Poisson Distributions

Binomial and Poisson Calculator

The binomial distribution describes the number of successes ($k$) in a fixed number of independent trials ($n$), each with a success probability $p$.

$$ P(X=k) = \binom{n}{k} p^k (1-p)^{n-k} $$

Trials (n):

Probability (p):

Successes (k):

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The Poisson distribution expresses the probability of a number of events ($k$) occurring in a fixed interval, given an average rate $\lambda$.

$$ P(X=k) = \frac{\lambda^k e^{-\lambda}}{k!} $$

Average rate ($\lambda$):

Events (k):

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$a$ (First Term):

$d$ (Common Diff.):

$n$ (Term Number):

$a$ (First Term):

$r$ (Common Ratio):

$n$ (Term Number):