Binomial Table

HISTORY

See binomial distribution.

MATHEMATICAL ASPECTS

Let the random variable X follow the binomial distribution with parameters n and p. Its probability function is given by:

$$ \begin{aligned} P (X = x) = C_n^x \cdot p^x \cdot q^{n-x}\:,\\ x = 0,1,2,\ldots,n\:, \end{aligned} $$

where C _n ^x is the binomial coefficient, equal to ${ \frac{n!}{x!(n-x)!} }$, parameter p is the probability of success, and ${ q = 1 - p }$ is the complementary probability that corresponds to the probability of failure (see normal distribution).

The distribution function of the random variable X is defined by:

$$ \begin{aligned} P(X \leq x) = \sum_{i=0}^x C_n^i \cdot p^i \cdot q^{n - i}\:,\\ 0 \leq x \leq n\:. \end{aligned} $$

The binomial table gives the value of ${ P(X \leq x) }$ for various combinations of x, n and p.

For large n, this calculation becomes tedious....