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Chapter 5: Q.5.3 (page 215)
Show that if has density function, then
Hint: Using Theoretical Exercise, start withand then proceed as in the proof given in the text when
Therefore,
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With being the probability that a normal random variable with mean and variance is less than , which of the following are true:
(a)
(b)
(c)
Prove Corollary.
Compute the hazard rate function of when is uniformly distributed over.
You arrive at a bus stop at a.m., knowing that the bus will arrive at some time uniformly distributed between and .
(a) What is the probability that you will have to wait longer than minutes?
(b) If, at , the bus has not yet arrived, what is the probability that you will have to wait at least an additional minutes?
Your company must make a sealed bid for a construction project. If you succeed in winning the contract (by having the lowest bid), then you plan to pay another firm $100,000 to do the work. If you believe that the minimum bid (in thousands of dollars) of the other participating companies can be modeled as the value of a random variable that is uniformly distributed on (70, 140), how much should you bid to maximize your expected profit?
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