Answer microeconomics questions below

A random sample of eight observations from a distribution are given below: 4.8 l 1.2 3.5 2.9 [LB {L5 2.3 [i] Derive the method of moments estimators for: [a] 3. from an Erpi) distribution [h] P from a g3 distribution. [4] (ii) Derive the method of moments estimators for: [a] k and p from a Type 2 negative binomial distribution [b] p! and 0'2 from a lognonnal distribution. [[5] [Total l'] 4 You have been given the following data Farmers Doctors age-group central exposed deaths central exposed deaths to risk to risk 60-75 8.453 83 25,858 345 65-70 6,886 161 11,793 351 70-75 6,310 521 4,540 123 total 21,649 765 12,191 1,119 crude central death rate 0.03534 0.02652 (i) Calculate the directly-standardised mortality rates for each occupation (between ages 60 and 75) with their estimated standard deviations, using the following standard population: age-group population 60-65 5,000 65-70 4.000 70-75 3,000 (ii) Calculate the corresponding SMR's and their estimated standard errors, using the follow- ing standard central death rates: age-group central death rate 60-65 0.0170 65-70 0.0283 70-75 0.0461 (iii) The crude age-specific death rates are all lower for the farmers, but the SMR is not. Could this feature arise in respect of R" or the CMF? 5 A medical statistician is investigating a certain rare disease o, which she considers not to be infectious. She is given the following date in respect of men aged 40 last birthday (1.b. ) in the country with which she is concerned. mid-year year estimate of no. of deaths population by cause o 1997 150,686 4 1998 145,890 1999 141,912 Find an approximate 99% confidence interval for the true central rate of mortality from this cause at age 40 1.b. in 1997-1999