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) = Ore /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 nr 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 0 =s n-m mf (c ) 1 - F(c) C C where s = rnr and F(c) = >f(x). r=1 T=0