Question: Fix r and p and let P(k), k = 0, 1, . . denote the probabilities in the negative binomial (r, p) distribution,
a) Show that the consecutive odds ratios are P(k)/P(k - 1) = (r + k -1) q/l (k = 1, 2, . . .)
b) Find a formula for the mode m of the negative binomial distribution.
c) For what values of r and p does the distribution have a double maximum? Which values k attain it?