Join Eddie Davila for an in-depth discussion in this video Normal curve, part of Statistics Foundations: Probability.
- Discrete distributions tend to look like this. We can use bar charts because each value is discrete. All numbers are whole numbers. But when you have continuous random variables, there are an infinite number of possible outcomes. Here are the wait times for 10 random travelers on a single day at an airport. No whole numbers and no repeated numbers. And I'm guessing that if we had data for 50 more travelers, it's very possible there still would not be any repeated values. In cases like this, we can say that the possible outcomes are infinite. Bar charts wouldn't work here, so instead we use curves to illustrate the distribution of outcomes. These curves are called probability densities. The area under the curve represents the probability of each and every outcome. So for this probability density, the probability of outcome A is X. The probability of outcome B is Y. Also since the area under the curve represents every possible outcome, the entire area under the curve is equal to 1.0, or a hundred percent. Again, we have endless possible outcomes, so the probability of any single scenario really isn't that interesting. Does anybody really care what's the exact probability of getting through security in exactly 12.5 minutes? This is why most of the time, people will calculate the probability of a group of outcomes. So let's go back to our distribution chart. Maybe a more interesting question might be, what's the probability of it taking between 10 and 20 minutes to get through airport security? It looks like the area under the curve in this section represents about 25% of the area under the curve. Now, if we change the question, what's the probability of it taking between 10 minutes and 40 minutes to get through airport security? Now we can see this is easily over 50% of the area under the curve, which means over 50% of customers get through security in 10 to 40 minutes. And of course, if we asked, what's the probability of it taking between one minute and 60 minutes to get through airport security? It would be very close to a hundred percent. I know, I'm being vague with my answers. You're probably wondering, how do we calculate the exact area under the curve in these intervals? for that, we would need two things. The formula of the curve and calculus, taking an integral. Yeah, that's probably a bit more than we can cover today. Still, we saw a few important things. The total area under the curve is 1.0. It represents 100% of all outcomes. We identified the probability of different events using the curve, and we were able to use the curve to estimate the probability of a range of outcomes. Since we're talking about probability densities and curves, let's now learn about one of the most famous curves of all, the bell-shaped curve.
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.