Question

Problem 2.1 The Poisson distribution and flying bombs

The following table lists the number of cells that were observed to have $k$ hits (this is Clarke's actual data!).

number of hits ($k$)	0	1	2	3	4	5 and over
number of cells with $k$ hits	229	211	93	35	7	1

(d) Use the estimate $\hat{\lambda}$ to predict the expected number of cells with $k$ hits, for $k \in \{0, 1, 2, 3, 4, 5+\}$. Compare the expected counts with the observed data. What conclusions can you make?