Probability Distributions

In our study of probability thus far, we've focused on events described as statements such as “getting a head when flipping a coin” or “incurring a profit in a trade.” While these statements capture the essence of events, they don't provide a numerical depiction of their nature or extent. They tell us “how likely” an event is to occur, but don't describe “how much” or “to what extent”. For example, knowing the probability of rain in an area is different from quantifying the amount of rain in that area. Herein lies the role of Random Variables. They act as a pivotal tool, allowing us to map every possible outcome of an event—whether continuous like heights, or discrete like dice rolls—to real numbers. But once we have these numbers, another question arises: How do we evaluate the probabilities of these specific numerical outcomes? This is where Probability Distributions come into play, offering a framework to understand the probabilities associated with the outcomes of each quantified event.  

In this chapter, we transition from the fundamental question of “what's the probability of an event happening?” to “what magnitude does an event take on when it occurs?” through the lens of Random Variables. We then deepen our exploration to determine “how probable is each distinct magnitude or outcome of that event?” utilizing Probability Distributions.

In this chapter, you will find various probability distribution charts, which have been created using Excel and third party tools in the background. However, we did not delve into the implementation of these charts using Excel or any other tools, as our primary goal is to provide a thorough understanding of the fundamental concepts by keeping them tool-agnostic.