What is the maximum number of buckets that could each

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online