AP Statistics Lectures

by Arnold Kling

Uniform Distribution

A uniform distribution is a distribution of a continuous variable in which the probability of X falling within a given interval is proportional to the size of the interval.

For example, if X is uniformly distributed between 0 and 1, then the probability that X will be between 0.3 and 0.4 is .1, because there are ten intervals of width .1 each. The probability of X falling between 0.1 and 0.25 is .15.

If X is uniformly distributed between 0 and 2, then what is the probability that X will fall between 0.3 and 0.4? Between 0.1 and 0.25?

Uniform distributions do not occur very often in nature. However, random number generators often are built to simulate the uniform distribution.

We can use a uniform random number generator to determine the winner of a raffle. Suppose that we have 247 entries, numbered one through 247. We can choose a random number between 0 and 1, multiply it by 247, and then round it to the the nearest integer in order to pick the winner.