Chapter 5: What’s Math Got To Do With It? The Power of Probability Distributions
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Chapter 5: What’s Math Got To Do With It? The Power of Probability Distributions
Overview
“Probability theory is nothing but common sense reduced to calculation.”
—Pierre-Simon Laplace
A “probability distribution” is one of the most significant concepts ever devised in mathematics. In an uncertain context, we can’t predict the outcome 100 percent of the time. If we’re trying to predict the next roll of a die, or the outcome of a sports game, we will get it right sometimes, but not all the time. What if we had a way to express the probabilities of the different outcomes? From there, we can then calculate useful results, like the most likely outcome, or other useful quantities like the variance (which you’ll look at shortly).
Chapter 1 explained that the two kinds of uncertainty are epistemic and aleatoric. Epistemic uncertainty exists because of a lack of knowledge. For example, let’s say that we are using a medical instrument to take some blood measurements. We want to use these measurements to predict whether someone has contracted a serious virus. These measurements are not 100 percent accurate. In fact, we know that any measurement could be around 20 percent off. In ten years’ time we might have developed an instrument that is more precise—say only 10 percent off. This is epistemic uncertainty.
In a coin-tossing experiment, we face aleatoric uncertainty. Assuming the coin is fair, whether it lands on heads or tails is a random phenomenon. Likewise, we can’t know what the result will be before someone rolls the die. The word “epistemic” comes from the Greek for “knowledge,” episteme; “aleatoric” comes from the Latin word for a die, alea—or aleator, a dice player. It’s a useful way to remember the distinction.
