Question

A discrete uniform distribution results from recording the final digit of the cell phone number for 3,000 students. What is the mean of this distribution?

Answer 1

In a uniform distribution, the mean is the average of the two end points. In this situation, all the numbers from zero to nine are equally likely to be the final digit of a cell phone number, then the mean is 4.5, i.e. `(9-0)/2`. We know that all the numbers [0,9] are equally likely to be the last digit, because we are told that the we have a "discrete uniform distribution".

Here's another example. Assume it's true that the average number of children in a household is uniformly distributed between one and five, i.e. the number of children in a household could be either one or two or three or four or five. And, moreover, each of these is equally likely to occur, i.e. in 20% of households there is one child, in 20% there are two and so on.

The average number of children in households across America, then, is `(5-1)/2=3`.