Question

The time spent waiting at a stoplight, assuming a positive amount of time is spent waiting and that the stoplight is on a timer and does not use a car sensor, can be well modeled by a uniform distribution. Suppose the time (in minutes) you spend waiting at a particular stoplight can be modeled by a Unif([0,2]) distribution. Compute and compare the average (expected value) and median amount of time you spend at the stoplight, and sketch the pdf of the distribution.

Answer 1

the mean and median = 1

Explanation:

From the question we have a uniform distribution

We define

a = 0

b = 2

In a uniform distribution, we have the mean and the median to be one and the same, that is equal.

Mean = median = (a+b)/2

= 2/2 = 1

So the expected value (mean) and median amount of time spent at the particular spotlight is 1 and the same.

Then the probability density function, pdf, of the distribution

= 1/(b-a)

= 1/2

0 ⩽ x ⩽ 2

Please check attachment for the sketch. Thank you