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Chapter 5: Q:5.3 (page 217)
For some constant c, the random variable X has the probability density function:
Find
a. The value of
b.
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Let be a random variable that takes on values betweenand. That is.Show that
Hint: One approach is to first argue that
localid="1646883602992"
and then use this inequality to show that
If is an exponential random variable with a parameter, compute the probability density function of the random variable defined by
Twelve percent of the population is left handed. Approximate the probability that there are at least lefthanders in a school of students. State your assumptions.
Evidence concerning the guilt or innocence of a defendant in a criminal investigation can be summarized by the value of an exponential random variable X whose mean 渭 depends on whether the defendant is guilty. If innocent, 渭 = 1; if guilty, 渭 = 2. The deciding judge will rule the defendant guilty if X > c for some suitably chosen value of c.
(a) If the judge wants to be 95 percent certain that an innocent man will not be convicted, what should be the value of c?
(b) Using the value of c found in part (a), what is the probability that a guilty defendant will be convicted?
The lung cancer hazard rateof a -year-old male smoker is such that
Assuming that a -year-old male smoker survives all other hazards, what is the probability that he survives to
ageand age 60 without contracting lung cancer?
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