Question 3.1 A random sample of eight observations from a distribution are given below: 4.8 7.6 1.2 3.5 2.9 0.8 0.5 2.3 (i) Derive the method of moments estimators for: (a) A from an Exp(A) distribution (b ) v from a Xy distribution. [4] (ii) Derive the method of moments estimators for: (a) k and p from a Type 2 negative binomial distribution (b) # and of from a lognormal distribution. [6] [Total 10] Question 3.2 A random sample from a Beta(a, ) distribution has a mean of 0.8 and a standard deviation of 0.3. Derive the method of moments estimates of a and B. [5]The production function for a firm is given as Q =12LK'S . If the firm wants to produce an output of 240 units, find the optimal values of labour and capital that will minimize the total cost of production given that labour cost per unit is 25 dollars and capital cost per unit is 50 dollars