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topjm [15]
2 years ago
6

Suppose you are taking the bus home, and can take either Route 51 or Route 82. You know that the Route 82 will arrive at the bus

stop in exactly 5 minutes, but because Route 51 is unreliable, you believe that the amount of time until it arrives is uniformly distributed between 0 and 20 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:
kykrilka [37]2 years ago
8 0

Answer:

E[T] = 10

Step-by-step explanation:

A distribution is called uniform if each outcome has the same probability of happening.

The uniform distribution has two bounds, a and b, and the expected value of the uniform distribution is given by:

E = \frac{a+b}{2}

Uniformly distributed between 0 and 20 minutes.

This means that a = 0, b = 20

Let T be the number of minutes you wait until you board a bus. Find E[T].

This is

E[T] = \frac{a + b}{2} = \frac{0 + 20}{2} = 10

E[T] = 10

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