Question

A particular area in a town suffers a high burglary rate. A sample of 100 streets is taken,
and in each of the sampled streets, a sample of six similar houses is taken. The table below
shows the number of sampled houses, which have had burglaries during the last six months.

No. of houses burgled x	0	1	2	3	4	5	6
No. of streets f	39	38	18	4	0	1	0

(i) (a) State any assumptions needed to justify the use of a binomial model for the number of
houses per street which have been burgled during the last six months.
(b) Derive the maximum likelihood estimator of X bar, the probability that a house of the
type sampled has been burgled during the last six months.
(c) Determine the probabilities for the binomial model using your estimate of X bar, and,
without doing a formal test, comment on the fit.

(ii) An insurance company works on the basis that the probability of a house being burgled
over a six-month period is 0.18. Carry out a test to investigate whether the binomial
model with this value of p provides a good fit for the data.

NOTE:THERE WAS A MISTAKE ON (b) IT IS ESTIMATOR OF X BAR NOT ESTIMATOR OF P but i have corrected it

Answer 1