Section B (60 Marks) Answer only four questions from this section. All questions carry equal marks. Question 9: A continuous random variable , has a probability density function (pdf) given by: Where is a constant. Determine the: (a). value of . [4 marks] (b). . [4 marks] (c). expectation, . [3 marks] (d). variance, . [4 marks] Question 10: John sold food stuff to a certain school in March on weekly basis as follows: Week 1: He sold 20 kg of sugar (S), 30 kg of maize flour (M) and 10 kg of rice (R). Week 2: He sold 14 kg of sugar, 25 kg of maize flour and 18 kg of rice. Week 3: He sold 30 kg of sugar, 20 kg of maize flour and 5 kg of rice. Week 4: He sold 15 kg of maize flour and 10 kg of rice. If a kg of sugar costs shs. 4,000; of maize flour shs.3,000; and of rice shs. 3,500. (a). (i). Write a matrix for the food stuff quantity. (ii). Write a matrix for the cost. (b). By matrix multiplication, determine the value of the sales in each week. (c). If John made a profit of 25% by selling all the items, determine the total cost price of the items. [15 marks] Question 11: The table below shows the prices of some food items and their corresponding weights in years 2000, 2005 and 2010.
Section B (60 Marks) Answer only four questions from this section. All questions carry equal marks. Question 9: A continuous random variable , has a probability density function (pdf) given by: Where is a constant. Determine the: (a). value of . [4 marks] (b). . [4 marks] (c). expectation, . [3 marks] (d). variance, . [4 marks] Question 10: John sold food stuff to a certain school in March on weekly basis as follows: Week 1: He sold 20 kg of sugar (S), 30 kg of maize flour (M) and 10 kg of rice (R). Week 2: He sold 14 kg of sugar, 25 kg of maize flour and 18 kg of rice. Week 3: He sold 30 kg of sugar, 20 kg of maize flour and 5 kg of rice. Week 4: He sold 15 kg of maize flour and 10 kg of rice. If a kg of sugar costs shs. 4,000; of maize flour shs.3,000; and of rice shs. 3,500. (a). (i). Write a matrix for the food stuff quantity. (ii). Write a matrix for the cost. (b). By matrix multiplication, determine the value of the sales in each week. (c). If John made a profit of 25% by selling all the items, determine the total cost price of the items. [15 marks] Question 11: The table below shows the prices of some food items and their corresponding weights in years 2000, 2005 and 2010.