A probability distribution is defined in math by an equation. We call this equation a probability density function or PDF. For every number from negative infinity to infinity, the probability density function gives a probability that this number will be generated. Using math notation, X tilde D means the random variable X follows a probability distribution D. The capital P with a lowercase x vertical bar and capital D is read as the probability of x given D. So, what does it mean when we say the probability of x given D? Let’s say we have a number two that we observed from a dataset. We assume that the dataset follows a particular probability distribution such as the normal distribution. The equation P of x tells us how likely the random variable would take on the value two. This P of x outputs a number between zero and one which represents this probability. For instance, here is the standard normal distribution written as a fancy-looking capital N. The standard normal distribution has a mean of zero and a standard deviation of one, but what if you had a distribution that was not centered around zero? Or, what if you had a distribution that had a flatter wider distribution? These distributions can still be modeled by the same equation by adjusting its parameters. To describe these variations of the normal distribution, we can adjust two of its parameters. Calculate the mean of the data and assign that value to mu. Calculate the standard deviation and assign it to sigma. The resulting function approximates the distribution of our data.