Question

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].

Answer 1

E[T] = 10

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 = (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] = (a + b)/(2) = (0 + 20)/(2) = 10`

E[T] = 10