Isye 2027

# What is the maximum number of buckets that could each

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Unformatted text preview: mized k k at p = n . That is, pM L (k ) = n . A slightly diﬀerent approach to the computation here would be to note that pM L is also the maximum of the log-likelihood: ln pX (k ). We assumed that 1 ≤ k ≤ n − 1. But if k = 0 then the likelihood is (1 − p)n , which is maximized at p = 0, and if k = n then the k likelihood is pn , which is maximized at p = 1, so the formula pM L (k ) = n is true for 0 ≤ k ≤ n. Example 2.8.2 Suppose it is assumed that X is drawn at random from the numbers 1 through 1 n, with each possibility being equally likely (i.e. having probability n ). Suppose n is unknown but that it is observed that X = k, for some known value k. Find the ML estimator of n given X = k is observed. 1 Solution: The pmf can be written as pX (k ) = n I{1≤k≤n} . Recall that I{1≤k≤n} is the indicator function of {1 ≤ k ≤ n}, equal to one on that set and equal to zero elsewhere. The whole idea now is to think of pX (k ) not as a function of k (because k is the given observation), but rather, 1 as a func...
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## This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.

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