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Unformatted text preview: N ≥ K lottery tickets. There are exactly K winning tickets. Tom wins x turkeys. Provide a ML estimator for the number of tickets that he purchased. 1 6. [(5 + 5) + 5 = 15 pts] There are N lottery tickets with numbers 1 , 2 , . . . , N . 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 maximumlikelihood estimator T for N . Is the estimator unbiased? (Hint: If X is a random variable with values in N , then E ( X ) = ∑ k ≥ 1 P ( X ≥ k ).) (b) Calculate approximately for large N the normalized expected value E N ( T ) /N . (Hint: Think about what you have learned in calculus about Riemann sums.) 2...
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 Fall '08
 WEBER
 pts, ML estimator, Uncle Ezra

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