Answer all questions precisely. Please explain your answers fully.

Question one.

a) Define the term cross price elasticity of demand and explain its value for substitutes andcomplementary commodities.

b) Use the data in the table below to complete income elasticity through the arc elasticitymethod

Quanitity Income (Shs.) Price (Shs.)

100 5,000. 16

120. 6,000 16

Question Two.

Given the market model

P= Qs

Qd = 48 - 4P

Qs= -6 + 14P

FindP andQ

A random variable X has a Gamma distribution with parameters o and 1. (i) Show that the moment generating function of X, M x (t) , is given by: Mx (1) = 1 [3] (ii) Use this moment generating function to show that the mean and variance of X are given by and , respectively. [2] (iii) In the case when 20 is an integer, prove that 21X is a %% random variable. (3] [Total 8](i) In an opinion poll, a random sample is to be asked whether they favour closer ties with Europe. Determine the minimum sample size required to ensure that 95% confidence limits for the underlying population proportion are of the form "15% ", justifying any approximations used. [4] (ii) 1,000 people took the opinion poll in part (i). 30% said "Yes" to closer ties with Europe, 50% said "No" and 20% said "Don't know". Calculate 95% confidence intervals for the proportion of the whole population holding each opinion. [4] (iii) After an extensive advertising campaign by the government another opinion poll of 800 people was taken. Of those questioned, 35% said "Yes". (a) Obtain a 90% confidence interval for the difference in proportions favouring closer ties with Europe before and after the campaign. (b) Comment on your answer. [4] [Total 12]An office manager wants to analyse the variability in the time taken for her typists to complete a given task. She has given seven typists the task and the results are as follows (in minutes): 15, 17.2, 13.7, 11.2, 18, 15.1, 14 The manager wants a 95% confidence interval for the true standard deviation of time taken of the form o > k. Calculate the value of k . [4]