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

Whereas a continuous random variable can have any value (typically within a specific range), a discrete random variable has a finite number of possible values.

An example of a discrete random variable is the value obtained by rolling a standard 6-sided die, which has only the following possible values: 1, 2, 3, 4, 5, and 6. Another example of a discrete random variable is the fraction of the next 100 vehicles that pass my window that are blue trucks. This variable also has 101 possible values, ranging from 0.00 (none) to 1.00 (all). Generally, a discrete random variable is an integer, though it can also be a rational fraction.

The actual value of a continuous variable is frequently dependent on measurement accuracy. An example of a continuous random variable is the distance a ball rolled along the floor will travel before stopping. A continuous random variable can have any value (usually within a certain range); there are not a fixed number of possible values.