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].

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joaobezerra joaobezerra · Answer 1 · 2021-03-25T01:37:06+01:00

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:

[tex]E = \frac{a+b}{2}[/tex]

Uniformly distributed between 0 and 20 minutes.

This means that [tex]a = 0, b = 20[/tex]

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

This is

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

E[T] = 10