Question: There are N lottery tickets with numbers. However, N is unknown. In an unobserved moment, Uncle Ezra takes a ticket at random and memorizes its number. He puts it back, and repeats this experiment n times.

(a) Provide Uncle Ezra’s maximum-likelihood estimator T for N. Is the estimator unbiased? (Hint: If X is a random variable with values in N, then )

(b) Calculate approximately for large N the normalized expected value. (Hint: Think about what you have learned in calculus about Riemann sums.)