6.104 Automated drilling machine. Refer to the Journal of Engi- neering for Industry (Aug. 1993) study of an automated drilling machine, Exercise 3.67 (p. 120). The eight ma- chining conditions used in the study are reproduced here. Workpiece Dril Size Drill Speed Feed Rate Experiment Material (in.) (rpmm) (ipr) 1 Cast iron 25 1,250 011 2 Cast iron 2 1.800 005 3 Steel 25 3,750 {003 4 Steel 25 2,500 003 5 Steel 25 2,500 008 6 Steel 125 4,000 {0065 7 Steel 12 4,000 {009 8 Steel 125 3,000 010 Suppose that two of the machining conditions listed will detect a flaw in the automated system. Define X as the number of these two conditions with steel material, and define Y as the number of these two conditions with .25-inch drill size. a. Find the bivariate probability distribution p(x. y). b. Find the marginal probability distribution pa(y). . Find the conditional probability distribution py(x y) Hint: The total number of ways to get two conditions is a combination of 8 conditions taken 2 ata g 81 time ur[ I 28. 2 \"The 28 events in this sample space are (where the numbers correspond to the experiment number: 1.2 L3 14 15 16 17 1.8 23 24 25 26 2.7 28 34 35 36 37 38 45 46 47 48 56 57 58 6,7 68, 78