Before we study the logistic function, we will review the original function on which it is based, and which gives it some of its more general properties.
Essentially, when we talk about the logit function, we are working with the function of a random variable p, more specifically, one corresponding with a Bernoulli distribution.
Before explaining theoretical details it is worthwhile noting that a Bernoulli distribution is a random variable that:
Takes a value of 0 with a failure probability of q = 1 - p
Takes a value of 1 with a success probability of p
It can be expressed as follows (for a random variable X with Bernoulli distribution):
This is the kind of probability distribution that will represent the probability of occurrence of the events as binary options, just as we want to represent our variables (existence of features, event occurrence, causality of phenomena, and so on).