problem 60

(a): $n^{n}$
(b): $(\frac{2 n - 1}{n - 1})$
(c): The least likely bootstrap sample is one where $a_{1} = a_{2} = \dots = a_{n}$ . Such a sample occurs with probability $\frac{1}{n^{n}}$ . The most likely bootstrap sample is one where all the terms are different. Such a sample occurs with probability $\frac{n!}{n^{n}}$ . Thus, the ratio of the probabilities is $n!$