A1 We mentioned the use of the Poisson distribution for modelling the number of “events” that occur in a two-dimensional region. Assume that when the region R being sampled has area a(R), the number X of plants of a certain species occurring in R has a Poisson distribution with parameter λa(R) (where λ is the expected number of plants per unit area) and that nonoverlapping regions yield independent X’s. Suppose an ecologist selects n nonoverlapping regions R1, . . ., Rnand counts the number of plants of a that species found in each region. Which is the expression of the joint pmf (likelihood)? Which is the maximum likelihood estimator of λ.

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