Mean and Variance of Negative Binomial Distribution

A negative binomial models the number of trials  
  to achieve a desired number  
  of successes.
We can treat the negative binomial as a sequence of geometric sequences each with parameter  
, each sequence ending in a success. The expected number of trial until a success is achieved in  
  and since we require  
  successes we would expect to have to carry out  
Similarly the variance of a geometric distribution is  
  so the variance of a sequence of  
  such geometric distributions is  

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