Continuous uniform distribution

Here is a spinning wheel, that has a circumference exactly 1 metre. We will perform an experiment where we set the wheel spinning, and then stop it at a random time. The outer edge of the wheel has distance markers around its edge, showing the distance of that point around the circumference from the zero point. There is also a fixed pointer next to the wheel:

When we randomly stop the wheel, we will measure the position of the fixed pointer on the wheel circumference:

We will call this value X. In the example above, the wheel happens to have randomly stopped where X is about 0.15 (ie it is 15cm from 0.0 on the circumference). What do we know about X?

Continuous random variables

We call X a continuous random variable. Random means that its value cannot be predicted, although there are still certain things we know about X. Continuous means that it can take any value.

This makes X quite different from, say, throwing a dice. Although throwing a dice is random, we know the result will always be an integer from 1 to 6.