Unformatted text preview: he stop just after a bus leaves. What is the probability that you have to
wait at most 15 minutes for the next bus?
Sol) Let X denote the time to wait until the next arrival of a bus. Because X ∼ Exp(2), we have
P (X ≤ 0.25) = 1 − e−0.25×2 = 1 − e−0.5 (b) (4%) Suppose that the next bus has not arrived 15 minutes later when a second person comes along.
What is the probability that the newcomer will have to wait at least 15 more minutes?
Sol) The problem, in fact, wants to ﬁnd P (X > 0.5|X > 0.25). Since the exponential distribution
possesses memoryless property, we have
P (X > 0.5|X > 0.25) = P (X > 0.25) = e−0.5 7. The lifetimes (in months) before failing for transformers are random variables with survival function (i.e.,
2 reliability) R(t) = P (T > t) = e−t for t > 0.
(a) (4%) Johnny has two transformers — a brand new one, and a one-month old one. Which has a...
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- Fall '09
- Probability, Probability theory, probability density function