TITLE(Binomial @@ The Binomial Distribution)
USAGE(
dbinom(x, n, p)
pbinom(q, n, p)
qbinom(prob, n, p)
rbinom(nobs, n, p)
)
ALIAS(dbinom)
ALIAS(pbinom)
ALIAS(qbinom)
ALIAS(rbinom)
ARGUMENTS(
ARG(x,q @@ vector of quantiles.)
ARG(prob @@ vector of probabilities.)
ARG(nobs @@ number of observations to generate.)
ARG(n @@ number of trials.)
ARG(p @@ probability of success on each trial.)
)
VALUE(
These functions provide information about the binomial distribution
with parameters LANG(n) and LANG(p).  LANG(dbinom) gives the density,
LANG(pbinom) gives the distribution function LANG(qbinom) gives
the quantile function and LANG(rbinom) generates random deviates.
PARA
The binomial distribution has density
DEQN(p(x) = CHOOSE(n @@ x) SUP(p@@x) SUP((1-p)@@n-x)
  @@ p(x) = Choose(n,x) p^x (1-p)^(n-x))
for EQN(x = 0, LDOTS, n).
)
EXAMPLES(
# Compute P(45 < X < 55) for X Binomial(100,0.5)
sum(dbinom(46:54, 100, 0.5))
)
