Negative Binomial Distribution Mean Calculator

For a negative binomial distribution (with the PMF $$ P(X=x)=\binom{x+r-1}{x}(1-p)^r p^x,\quad x=0,1,2,\dots $$) where \(p\) is the failure probability and \(r\) is the number of successes, the mean (expected number of failures) is given by: $$ \mu = \frac{r\, p}{1-p}. $$

* Enter the number of successes \( r \) (integer \(\ge1\)) and the failure probability \( p \) (with \(0 < p < 1\)).