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12. Two friends have arranged to meet for dinner at a restaurant. Each person arrives indepen- dently of the other, with equal probability, at one of the following times: 6:30 PM, 7:00 PM, or 7:30 PM. Let X - the time, in minutes, that the first person to arrive has to wait for the other to arrive (hint: if both parties arrive at the same time, then X takes the value 0.) (a) What is the range of X? Answer: (0, 30, 60) (b) Give the probability distribution by assigning probabilities to the values in the range of X (c) What is the probability that they both arrive at 6:30 PM? Answer: 1/9 (d) What is the probability that the first person to arrive must wait exactly 30 minutes for the second person to arrive? Answer: 4/9 (4.1.5)

math   Statistics-And-Probability   
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