Question

Consider the special case of binomial distribution such that the probability of exactly k 'success' is given by: $p_k=\binom rk \frac{1}{n^k} (1-\frac{1}{n})^{r-k}$ . Prove that the most probable number is the the integer such that $\frac{r-n+1}{n}<v<\frac{r+1}{n}$ . In other words, $p_{v}$ is the largest where ranges from 0 to r.

Answer 1