Take -away BMA1104 BEDSC 1. A die is loaded such that the probability of a face showing up is proportion the face number. Determine 1/1 i). The probability of each sample point. (2mks) ii). The expectation and variance of the random variable that models this outcome. (5mks) 2. There are three manufacturing companies that make a product: Aberations, Brochmailians, and Chompielians. Aberations has a 50% market share, and Brochmailians has a 30% market share. 5% of Aberations' product is defective, 7% of Brochmailians' product is defective, and 10% of Chompieliens' product is defective. i). What is the probability a randomly selected product is defective? (5mks) ii). What is the probability that a defective product came from Brochmailians? (5mks) 3. Time X in hours between failures is a continuous random variable with a density f(x) = le-0.01x for x > 0 1 0 elsewhere Find A hence P(50 x $ 150) and P(x $ 100). (5mks) Q4.a). The following are the marks of student in two subjects determine the rank correlation coefficient of the performances in the two subjects and make a brief comment. (8mks) Candidates Math Accounts P 92 67 O 82 88 R 60 58 S 87 80 T 72 69 U 60 77 V 52 58 W 50 60 X 47 32 Y 59 54