Suppose a random variable has a frequency distribution that is Poisson with parameter . Suppose the parameter is also a random variable and it has a gamma distribution with parameters and . Then is equivalent to a negative binomial with parameters and .
- When , the gamma distribution is equivalent to an exponential distribution.
- This also means the negative binomial has parameter which is equivalent to a geometric distribution.
- What is the expected number of discoveries per year for a bot chosen at random?
- What is the variance?