We are asked to provide examples of probability distributions that are either discrete or continuous. Then we will be able to describe the difference between them. Let's start with a discrete distribution.
Discrete Distribution
An example of a discrete distribution is rolling a dice.
Here we have six possible outcomes that we can get each time we roll a dice. This means that the variable describing the possible outcomes for this situation is a discrete variable.
{1, 2, 3, 4, 5, 6 }
Therefore, a discrete distribution has a finite number of possible outcomes.
Continuous Distribution
In case of a continuous distribution, the variable describing the possible outcomes should be a continuous variable. Let's think of human height as an example. Take a look at the example female height distribution.
Here we have an infinite number of possible outcomes. Theoretically, height can be any positive number and we can measure to any number of decimal places of accuracy. Of course, the majority of the heights will be close to the average but still the set of possible values contain infinitely many possibilities.
Comparison
As we have seen, in a continuous distribution we have an infinite number of possible outcomes while in a discrete distribution we have a finite set of possible outcomes.
