. Suppose your waiting time for the campus shuttle in the morning is uniformly distributed on [0, 8), but the waiting time in the evening is uniformly distributed on [0, 15], independent of the morning time. (a) If you take the shuttle every morning and evening for a week, what is your total expected waiting time? (b) What is the variance of your total waiting time? (c) What are the expected value and variance of the difference between the morning and evening waiting times on a given day? (d) What are the expected value and variance of the difference between the total morning waiting timo ond e totel ouoning uoiting time in e giuon uool?

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1. Suppose your waiting time for the campus shuttle in the morning is uniformly distributed on [0, 8],
but the waiting time in the evening is uniformly distributed on [0, 15)], independent of the morning
time.
(a) If you take the shuttle every morning and evening for a week, what is your total expected
waiting time?
(b) What is the variance of your total waiting time?
(c) What are the expected value and variance of the difference between the morning and evening
waiting times on a given day?
(d) What are the expected value and variance of the difference between the total morning waiting
time and the total evening waiting time in a given week?
Transcribed Image Text:1. Suppose your waiting time for the campus shuttle in the morning is uniformly distributed on [0, 8], but the waiting time in the evening is uniformly distributed on [0, 15)], independent of the morning time. (a) If you take the shuttle every morning and evening for a week, what is your total expected waiting time? (b) What is the variance of your total waiting time? (c) What are the expected value and variance of the difference between the morning and evening waiting times on a given day? (d) What are the expected value and variance of the difference between the total morning waiting time and the total evening waiting time in a given week?
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