During the Second World War, London was hit by numerous flying bombs. The following data are from an area in South London of 36 square kilometers. The area was divided into 576 squares with sides of...

During the Second World War, London was hit by numerous flying bombs. The following data are from an area in South London of 36 square kilometers. The area was divided into 576 squares with sides of length 1/4 kilometer. For each of the 576 squares the number of hits was recorded. In this way we obtain a dataset x1, x2,...,x576, where xi denotes the number of hits in the ith square. The data are summarized in the following table which lists the number of squares with no hits, 1 hit, 2 hits, etc.

An interesting question is whether London was hit in a completely random manner. In that case a Poisson distribution should fit the data.

a. If we model the dataset as the realization of a random sample from a Poisson distribution with parameter µ, then what would you choose as an estimate for µ?

b. Check the fit with a Poisson distribution by comparing some of the observed relative frequencies of 0’s, 1’s, 2’s, etc., with the corresponding probabilities for the Poisson distribution with µ estimated as in part a.