 I rolled it 200 times times 200. Then the line would be at 33. So that would be one form of distribution where I could use that mathematical equation to predict what's gonna happen, even though it's not perfect. So then we have the Poisson distribution. Now this is the formula for the Poisson distribution, which you might say, oh my, this is gonna kill me. It's the Poisson distribution. But no, it's not that it's a Poisson distribution. And we're not too worried about the formula because the goal isn't that we need to be able to re-represent the formula. The point is that we have this genius that came up with the idea of the curve. And if we see certain characteristics in the data, it might be represented by a Poisson distribution, which we then can use Excel functions and whatnot to make future predictions using the formula. So don't be intimidated too much by the formula, but we will talk about it a little bit more in future presentations. The general idea is that it represents events and fixed intervals and examples are cars arriving at an intersection. So this is also often in a line waiting kind of situation where the Poisson distribution happens to work out. And remember, the idea here is, well, if I have these situations, these data sets that I'm looking at, is there a way that I can have a smooth curve that represents approximately the actual data set? Because if I can do that with a function, it will allow me to give me predictive power into the future. And it has been noticed that in business scenarios, a lot of times when you have these line waiting situations, you're waiting in line at the drive-through or at a roller coaster or cars arriving at an intersection that they seem to follow this Poisson distribution. We'll talk more specifically about characteristics that are typically present for data to follow a Poisson distribution. So if we plotted the data of cars arriving at intervals, say every minute interval, we count how many cars arrive at an intersection, then, and we then plot that data, we might observe that it is closely represented by the curve of a Poisson distribution. And if so, then we can use the Poisson distribution to approximate what is actually happening given us predictive power. So this is a graph of a Poisson distribution. We'll talk more about it when we get into Excel examples. But the general idea is that if you're talking about cars that are going into an intersection or if you're talking about line waiting situation and how many people are showing up to the line in any one-minute interval, then the upper limit is gonna be infinite, is the general idea. Now, in practice, you're not gonna have an infinite a number of people showing up to a line in any given situation, but in theory, it can go up forever. So this looks like a bell-shaped curve, but it's actually kind of skewed to the right. And that's gonna be the general characteristics of a Poisson distribution. It's gonna have this somewhat gentle right skewness to it. And we'll talk a little bit when we get to specifics problems on how the shape kind of changes as you change some of the parameters to it. The next one is the exponential distribution. So it represents time between events. And this one is often related to a Poisson distribution. So in other words, if you're looking at a line waiting situation, then the Poisson distribution is telling you or asking the question of how many cars are arriving in a certain interval of time or what are the likelihood that how many cars arrive in a certain interval of time, like a minute. The exponential distribution kind of flips that around. And now we're talking about the time between arrivals of individuals or cars. So it's a little bit more difficult, I think, for most people to kind of first wrap their mind around that relationship between the Poisson and the exponential distribution. The examples that we go through, I think will shed a lot of light onto that relationship. So we'll take a look at those in future presentations. But you also have radioactive decay is another common example of the shape of the distribution which we'll take a look at in a second here. Relation to Poisson times between Poisson events follow an exponential distribution. So if you notice a Poisson distribution on the events, the time between events, then you would expect to follow an exponential distribution which often happens in business scenarios with those line waiting situations. And it looks like this. So that's gonna be the exponential look that you'll be envisioning when you're thinking exponential. And I think the decay one, the decay of radioactive material kind of comes to mind to me oftentimes when I'm thinking about this shape that gives me the vision of this shape more than a line waiting situation which is a little more difficult to wrap your mind around at first. But the examples I think will help with that. Next, we have the binomial distribution. Now again, don't be intimidated by the equation. We wanna put the equation up top because, and we'll talk more about the equation later, but the equation isn't really the important thing. The idea, the important thing is