Introducing probability distribution

Probability distribution provides a framework for understanding and predicting the behavior of random variables. Once we know the underlying data-generating probability distribution, we can make more informed decisions about how things are likely to appear, either in a predictive or optimization context. In other words, if the selected probability distribution can model the observed data very well, we have a powerful tool to predict potential future values, as well as the uncertainty of such occurrence.

Here, a random variable is a variable whose value is not fixed and may assume multiple or infinitely many possible values, representing the outcomes (or realizations) of a random event. Probability distributions allow us to represent and analyze the probability of these outcomes, offering a comprehensive view of the underlying uncertainties in various scenarios. A probability distribution takes the random variable, denoted as x, and converts it...