Given independent Bernoulli trials with probability of success
, the frequency function of the number of trials until the -th success
This is called a negative binomial distribution
with parameter .
The frequency function and the cumulative distribution function (CDF)
are displayed up to
The geometric distribution is a special case of negative
binomial distribution when .
and identically distributed (iid) geometric random variables with parameter ,
then the sum
becomes a negative binomial random variable with parameter .
The frequency function and the cumulative distribution function
can be shown graphically.
Expectation, variance and mgf of negative binomial distribution.
By using the
sum of iid geometric rv's
we can compute the expectation, the variance, and the mgf of negative binomial
random variable .
What is the average number of times one must throw a die until
the outcome ``1'' has occurred 4 times?
Generated by MATH GO: 2005-11-16