A box contains four slips of paper marked 6, 7, 8, and 9. Two slips are selected without replacement. List the possible values for each of the following random variables shown below. (Enter your answers as comma-separated lists.) (a) x = sum of the two numbers 15,16,17,18,19 X (b) y = difference between the first and second numbers -3, - 2, - 1,1,2,3 (c) z = number of slips selected that show an even number 0,1,2 (d) w = number of slips selected that show a 9 0.1Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose that the probability distribution of y is as follows. y o 1 2 3 4 p(y] 0.61 0.21 0.11 0.05 7 (a) Only y values of O, 1, 2, 3, and 4 have positive probabilities. What is 11(4)? (Hint: Consider the properties ofa discrete probability distribution.) 9(4) = l0.01 ix (b) How would you interpret 11(1) : 0.21? O The probability of one randomly chosen carton having broken eggs in it is 0.21. G) In the long run, the proportion of cartons that have exactly one broken egg will equal 0.21. O The proportion of eggs that will be broken in each carton from this population is 0.21. O In the long run, the proportion that will have at most one broken egg will equal 0.21. (c) Calculate P(y S 2), the probability that the carton contains at most two broken eggs. pry : 2) =l l Interpret this probability. O The proportion of eggs that will be broken in any two cartons from this population is this probability. 6) In the long run, the proportion that will have at most two broken eggs will equal this probability. O The probability of two randomly chosen cartons having broken eggs in them is this probability. 0 In the long run, the proportion of cartons that have exactly two broken eggs will equal this probability. O The probability of two randomly chosen cartons having broken eggs in them is this probability. 0 In the long run, the proportion of cartons that have exactly two broken eggs will equal this probability. (cl) Calculate P(y