Source: Graphs by Katherine Williams
This tutorial covers probability distributions. A probability distribution is the description of all of the possible outcomes and their probabilities. And remember, an outcome is one specific thing that's going to occur. With this, it's pretty similar to a frequency distribution, and we've talked about those before and other tutorials.
Key things to look for when you're checking over probability distribution is that, first of all, the probabilities have to be between 0 and 1. This is true of every probability ever. It has to be between 0 and 1. So if you get a probability showing 1.1 or negative something, then you know there's an issue somewhere.
Secondly, the sum of all the probabilities-- when you add all of the outcomes together, that should total up to 1. Here we have an example of two ways of representing probability distribution. There's a lot of other options. You can also use mathematical formulas, or graphs look a little bit different than this.
The first part shows us a table. In this table, it's showing the list of the outcomes, the number of heads. You could get 0 heads, 1 head, or 2 heads. This table is talking about flipping a coin twice. When you flip a coin twice, you could get no heads that come up, you could have one had come up, or you could have two heads come up.
And right next to that, it tells us the probability of each of those outcomes happening-- a 0.25, a 0.5, and a 0.25. So first, all those probabilities are between 0 and 1, so that's good. Second, if I added those all up together, it would equal 1 exactly, which is also good. So this is an accurate probability distribution.
Over here, we have a graph displaying the same information. It lists the events across the bottom-- 0 heads, 1 head, and 2 heads. And on the side, it's showing us those probabilities-- 0.25, 0.5, 0.25. So again, all those probabilities displayed are between 0 and 1, and when you add them all together, you get 1.
When we're talking about probability distributions, we're talking about either continuous probability or discrete probability. We've used these where continuous and discrete and other tutorials, and here it takes on a similar meaning. With a continuous probability, there's an infinite number of outcomes. There's no differentiation between the two. There's no spaces here.
And because of that, you can't list individual outcomes. And because you can't list individual outcomes, you can't list them out on a table, so you cannot use a table to represent a continuous probability. Now, on the other hand, we have discrete probability distributions. Those have a finite number of outcomes. You can name the events specifically, so you can name those outcomes. And you can use a table there.
So for this first example, when we have a table, that's pretty obviously a discrete probability distribution. Similarly, our other example from before, because we can name the event specifically-- 0 heads, 1 heads, 2 heads-- we are naming specific outcomes, so we know it's discrete. An example of continuous is also something that we've seen before.
The normal curve is an example of a continuous probability distribution. We're not naming specific outcomes, like 0, 1, 2, 3. Instead, we're showing all the full range of what could happen. Decimals are possible-- even teeny, teeny, tiny decimals. Those are things that are possible here. So this has been your introduction to probability distributions.