Discovering common continuous probability distributions

Continuous probability distributions model the probability of random variables that assume any value within a specific continuous range. In other words, the underlying random variable is continuous instead of discrete. These distributions describe the probabilities of observing values that fall within a continuous interval, rather than equal to individual discrete outcomes in a discrete probability distribution. Specifically, in a continuous probability distribution, the probability of the random variable equal to any specific value is typically zero, since the possible outcomes are uncountable. Instead, probabilities for continuous distributions are calculated for intervals or ranges of values.

We can use a PDF to describe a continuous distribution. This corresponds to the PMF of a discrete probability distribution. The PDF defines the probability of observing a value within an infinitesimally small interval around a given...