Exploring common discrete probability distributions
Discrete probability distributions are characterized by their corresponding PMFs, which assign a probability to each possible outcome of the input random variable. The sum of the probabilities for all possible outcomes in a discrete distribution equals 1, leading to ∑ i=1 C f( x i) = 1. This also means that one of the outcomes must occur, giving f(x i) > 0, ∀ i = 1, … , C.
Discrete probability distributions are vital in various fields, such as finance. They are commonly used for statistical analyses, including hypothesis testing, parameter estimation, and predictive modeling. We can use discrete probability distributions to quantify uncertainties, make predictions, and gain insights into the underlying data-generating process of the observed outcomes.
Let’s start with the most fundamental discrete distribution: the Bernoulli distribution.
