What is a probability distribution?

The definition of the word `distribution’ refers to how something is shared out in a group or how it is spread out over an area. Notice that sharing out in a group is discrete and spreading over an area is continuous. We saw the definition of discrete and continuous in …

Analogously to these definitions, we can also have discrete and continuous probability distributions. Let X be a random variable – a variable whose possible values are the outcomes of a random event. X could be a discrete random variable whereby its possible values belong to a discrete set of outcomes. For example, the number of times a head comes up when a coin is tossed 10 times is a discrete random variable (this is also finite and restricted to integers between 0 and 10 inclusively).  Likewise, X could be a continuous random variable where it can take on not just discrete values but anything in between. In this case, consider the random variable X whose value is the weight of a survey participant randomly selected in public. This is an example of a continuous random variable  (although values outside of typical are more unlikely, the possible values are continuous and not as finite as the discrete case illustrated above).

A Discrete Probability Distribution

…

A Continuous Probability Distribution

…