What is the difference between a discrete random variable and a continuous random variable?

A discrete random variable has a finite number of possible values. A continuous random variable could have any value (usually within a certain range).

A discrete random variable is typically an integer although it may be a rational fraction. As an example of a discrete random variable: the value obtained by rolling a standard 6-sided die is a discrete random variable having only the possible values: 1, 2, 3, 4, 5, and 6. As a second example of a discrete random variable: the fraction of the next 100 vehicles that pass my window which are blue trucks is also a discrete random variable (having 101 possible values ranging from 0.00 (none) to 1.00 (all).

A continuous random variable could take on any value (usually within a certain range); there are not a fixed number of possible values. The actual value of a continuous variable is often a matter of accuracy of measurement. An example of a continuous random variable: how far a ball rolled along the floor will travel before coming to a stop.