Help in solving the following questions.

The mortality rates for a population for the age range 30-34 were estimated by fitting a straight line o + 8x to the crude values of log, (q,/p. ). Test whether this model (with estimated parameter values of a =-10.9446 and =0.110404) can be considered to give a good fit to the data shown in the table below for 2003. Agc x 30 31 32 33 34 Number of deaths in 2003 335 391 428 436 458 The initial exposed to risk in 2003 was approximately 700,000 at each age.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 2 3 4 5 6 No. of streets 39 38 18 4 0 0 (1) (a) State any assumptions needed to justify the use of a binomial model for the number of sampled houses per street which have been burgled during the last six months. (b) Derive the maximum likelihood estimator of p. the probability that a house of the type sampled has been burgled during the last six months. (c) Fit the binomial model using your estimate of p, 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