In bacterial counts with a haemacytometer, the number of bacteria per quadrat has a Pois- son distribution with probability mass function f(x), where f(x) = 0Te-® /x! and 0 is to be estimated. If there are many bacteria in a quadrat, it is difficult to count them all, and so the only information recorded is that the number of bacteria exceeds a certain limit c, a large positive integer. In a random sample of n quadrats, it was observed that ng quadrats had x bacteria (x = 0,1, · ·,c) and that m quadrats had more than c bacteria. Show that the maximum likelihood estimate of 0 is given by 1 mf(c) = s In - m - where s = an, and F (c) Σf(a). x=1 x=0

In bacterial counts with a haemacytometer, the number of bacteria per quadrat has a Pois- son distribution with probability mass function f(x), where f(x) = 0Te-® /x! and 0 is to be estimated. If there are many bacteria in a quadrat, it is difficult to count them all, and so the only information recorded is that the number of bacteria exceeds a certain limit c, a large positive integer. In a random sample of n quadrats, it was observed that ng quadrats had x bacteria (x = 0,1, · ·,c) and that m quadrats had more than c bacteria. Show that the maximum likelihood estimate of 0 is given by 1 mf(c) = s In - m - where s = an, and F (c) Σf(a). x=1 x=0

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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