1. Differentiate between the additive model and the multiplicative model as used in time series analysis 2. Distinguish between probability sampling and non probability sampling methods 3. The sales data of XYZ Ltd (in millions of shillings) for the year 2011 to 2014 inclusive are given below. Quarter Year 1 2 3 4 2011 40 64 124 58 2012 42 84 150 62 2013 46 78 154 96 2014 54 78 184 106 Required 1. The trend in the data using moving average method The estimated sales for each quarter of the year 2014 4. The following are the daily wages in Kish. of 30 workers of a flower farm in Ruiru, which grow the flowers and export them to European Countries 140 139 126 114 100 88 62 77 99 103 108 129 144 148 134 63 69 148 132 118 142 116 123 104 95 80 85 106 123 133 The Company (flower farm ) gives bonus of Sh. 10, 15, 20, 25, 30 and 35 for individuals in the respective salary ; exceeding 60 but not exceeding 75, exceeding 75 but not exceeding 90 and so on up to exceeding 135 but not exceeding 150 Required to calculate 1. The average wage and average bonus paid by the flower farm The median wage and median bonus iii. The modal wage and modal bonus iv . The standard deviation for the wages and also for the bonus 5. A woven cloth is liable to contain faults and is subjected to an inspection procedure. Any fault has a probability of 0.7 that it will be detected by the procedure , independent of whether any other fault is detected or not . Required: ) If a piece of cloth contains three faults , A, B and C, 1 ) Calculate the probability that A and C are detected , but that B is undetected ; ii) Calculate the probability that any two of A, B and C be detected, the other fault being undetected