4. Students arrive at a tutoring center to a Poisson process with a mean of 8 per hour. (a) What is the probability that

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4. Students arrive at a tutoring center to a Poisson process with a mean of 8 per hour. (a) What is the probability that the second arrival is observed less than 10 minutes after the first arrival? (1 point) (b) What is the probability that the third arrival is observed less than 10 minutes after the second arrival if the it has not yet been observed 5 minutes after the first arrival? (1 point) (c) What is the probability that more than 12 minutes is required for the second arrival? (2 point) (d) Suppose a volunteer working at the center has a 4-hour shift. Compute the expected value and the variance for the number of students who would arrive during her shift. (1 point)