Probability distributions

You've probably seen a chart such as the following one; it's showing us the values that appear in a dataset, and how many times those values appear. This is called a distribution of a variable. In this particular case, we're displaying the distribution with the help of a histogram, which shows the frequency of the variables: 

In this section, we're interested in a particular type of distribution, called a probability distribution. When we talk about probability distributions, we're talking about the likelihood of a random variable taking on a certain value, and we create one by dividing the frequencies in the preceding histogram by the total number of samples in the distribution, in a process called normalization. There are two primary forms of probability distributions: probability mass functions for discrete variables, and probability density functions for continuous variables, as well as; cumulative distribution functions, which apply to any random variables, also exist.