Join Eddie Davila for an in-depth discussion in this video Discrete vs. continuous, part of Statistics Foundations: Probability.
- For this chapter, there are three new terms we'll need to understand. Random variable, discrete, and continuous. Let's begin with a random variable. Why random? Why do we use that word? Well, as we perform experiments, we need to understand that the value of the eventual outcome of an experiment is unknown or random. This is why we call the result of an experiment a random variable. The amount of rain that will fall in London this month is a random variable. The length of time you will wait in line at Starbucks tomorrow, that, too, is a random variable. As is the number of drinks the 10th customer of the day orders. These random variables can either be discrete random variables or continuous random variables. Let's begin with discrete random variables. The number of drinks the next Starbucks customer will order is very likely as low as zero. Perhaps they just want a food item, but probably no larger than 10. And since they can't order half drinks, the outcome has to be a whole number. This is an example of a discrete random variable. The same thing goes for the sum of dots on a single roll of two dice. The only possibilities are two through 12. Again, we do not have any decimals. This, too, would be a discrete probability. So, what our continuous random variables? Consider the amount of rainfall in London for the month of October. It might end up being 0.58 inches. It might be 2.35 inches. It might even be 4.777 inches. There really is no end to the possible rain outcomes for this month. The same goes for your wait at Starbucks tomorrow. You might wait 36 seconds, four minutes and 17 seconds, or perhaps they are very busy and you end up waiting 10 minutes and 33 seconds. Again, the possibilities are endless. As you can see, continuous random variables don't have to be whole numbers. So, minus a few very odd exceptions, they can have almost any value. Discrete random variables have very limited outcomes. Random variables have limitless possible outcomes. Thus, each will require different probability techniques, but before we delve into discrete and continuous random variable probabilities, look around you. Consider your company. Think of your favorite sport or maybe think about environmental data. Can you identify discrete random variables and continuous random variables in your life and in the world around you? And as you do that, start to think about how probabilities are calculated and discussed differently in each of those scenarios.
Eddie explains that probability is used to make decisions about future outcomes and to understand past outcomes. He covers permutations, combinations, and percentiles, and goes into how to describe and calculate them. Eddie introduces multiple event probabilities and discusses when to add and subtract probabilities. He describes probability trees, Bayes’ Theorem, binomials, and so much more. You can learn to understand your data, prove theories, and save valuable resources—all by understanding the numbers.