Sebaran binomial négatip: Béda antarrépisi

The statement that the sum from ''x'' = ''r'' to infinity, of the probability Pr[''X'' = ''x''], is equal to 1, can be shown by a bit of algebra to be equivalent to the statement that (1 − ''p'')^{− ''r''} is what [[binomial series|Newton's binomial theorem]] says it should be.

 

 

Thus the negative binomial distribution bears the same relationship to the negative-integer-exponent case of the binomial theorem that the binomial distribution bears to the positive-integer-exponent case.