The Binomial Distribution
In many cases, it is appropriate to summarize a group of independent observations by the
number of observations in the group that represent one of two outcomes. For example, the
proportion of individuals in a random sample who support one of two political candidates fits
this description. In this case, the
statistic
is the
count X of voters who support
the candidate divided by the total number of individuals in the group
n. This provides an
estimate of the
parameter p, the proportion of
individuals who support the candidate in the entire population.
The corresponding graphs for the probability density function and cumulative distribution function
for the B(20,1/6) distribution are shown below:
Since the probability of 2 or fewer sixes is equal to 0.3287, the probability of rolling more than
2 sixes = 1 - 0.3287 = 0.6713.
The probability that a random variable X with binomial distribution B(n,p) is
equal to the value k, where k = 0, 1,....,n , is given by
clipped from: www.stat.yale.edu 
