Note: Solve all questions and submit within the stipulated time, partial credit will be given otherwise. Q. No. 1: Ted Olson, the director of Overnight Delivery, Inc., has become concerned about the number of first-class letters lost by his firm. Because these letters are carried by both truck and airplane, Mr. Olson has broken down the lost letters for the last year into those lost from trucks and those lost from airplanes. His data are as follows: Number Lost from J F M A M J .i A S 0 N D Truck 4 S 2 3 2 I 3 5 4 'r' 0 I Airplane 5 6 0 2 l 3 4 2 4 7 4 0 Mr. Olson plans to investigate either the trucking or air division of the company, but not both. If he decides to investigate the division with the highest expected number of lost letters per month, which will he investigate? [1. No. 2: From a lot of 10 missiles, 4 are selected at random and fired. If the lot contains 3 defective missiles that will not fire, what is the probability that (al all 4 will fire? (bl at most 2 will not fire? Q. No. 3: The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width, is given by J.' U l 2 3 4 0.41 0.37 {1.16 0.05 0.01 Find the probability of waiting less than 12 minutes between successive speeders (a) using the cumulative distribution function of X; (b) using the probability density function of X