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timurjin [86]
3 years ago
15

Suppose you are taking the bus home, and can take either the 51 or the 82. you know that the 82 will arrive in exactly 10 minute

s, but because the 51 is unreliable, you suspect that the amount of time until it arrives is uniformly distributed between 0 and 30 minutes. you take the first bus that arrives. let t be the number of minutes you wait until you board a bus. find e[t].
Mathematics
1 answer:
elena55 [62]3 years ago
8 0
We are dealing here with a uniform distribution ranging from 0 to 30 minutes.  We need to calculate the probability that the unreliable bus will arrive before the reliable one.  This probability is the area under the uniform distribution "curve" from 0 to 10 minutes.  This constitutes 1/3 of the entire unform distr. curve.  So the probability that the unreliable bus will arrive before the reliable one is 1/3, or 0.33.  The probability that it will arrive AFTER the reliable bus is 2/3, or 0.67.
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Step-by-step explanation:

Okay so I will explain the first one.

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Answer:

a) P=0.2503

b) P=0.2759

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Step-by-step explanation:

We have this information:

25% of American households have only dogs (one or more dogs)

15% of American households have only cats (one or more cats)

10% of American households have dogs and cats (one or more of each)

50% of American households do not have any dogs or cats.

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