MAT 210 Final, Spring 2016

MAT 210 1. (10 pts — 5 pts each) In a certain assembly plant, three machines M), Mz, M3 make 40%, 50% and Li of the product respectively. From past experience, it is known that 5%, 6% and 10% of the items produced by the machines M), Mz and M3 respectively are defective. a) Suppose that an item is randomly selected from the product, what is the probability that it is non defective? b) [fan item was randomly selected from the product and found to be non defective, what is the probability that it was produced by machine M;? . (LO0pts —5 pts each) The probability that any vehicle will turn left at a particular intersection is 0.4. The left-turn lane at this intersection has rooms for three vehicles only. a) If five vehicles arrive at this intersection while the light is red, find the probability that the left-turn lane will hold all the vehicles that want to turn lett. b) Find the probability that six vehicles must arrive at the intersection while the light is red to fill up the lefi-tum lane. . (LOpts-Spts eachjLet x denote the number of “do-loops” in a Fortran program and the number of runs for a novice to debug the program Assume that the joint density for (x,y) is given by: l 2 3 4 0.059 0.100 0.050 0.001 0.093 0.120 0.082 0.003 0.065 0.102 0.100 0.010 O.050 0.075 o.070 0.020 a) Find the probability that a randomly selected program contains at most one “do-loop™ and requires at least 2 runs to debug the program b) Find the correlation between x & y 4. (10pts-Spts each)A computer firm introduces a new home computer. Past experience shows that the random variable x, which is the time of peak demand measured in months after its introduction, follows a Gamma Distribution with variance 36. a) If the expected value of v is 18 months, find a & £ b)Find P(13.7 <x <= 31.5) §. (15 pts-Spts each) Let X and Y denote the lengths of life, in years, of two components in an electronic device. Assume that the joint density for (x,y) is given —(x+y) e , x>0, y>0 by f(x,y) = : 0 otherwise