Welcome to the small tutorial on exponential distribution or how to use exponential distribution values in Excel. Exponential distribution is probably the second most important distribution. It is usually used to model what are called inter arrival times for a process. So for example, consumers arrival or customer arrival at a shop or arrivals of cars at an intersection. Whatever your modeling needs are, where there is an arrival process that occurs. Unlike normal distribution, Exponential distribution just takes one parameter value, which is called the arrival rate. The arrival rate is typically represented by a Greek symbol Lambda. So just like normal distribution, we can model this using an Excel function which is called expon.dist And again, like we did in normal distribution, we'll provide it some parameter values. The first parameter is the value at which you want to get the probability, or at or around that value, as I explained in the last video, I'm again going to put a dollar sign in front of A so that we can copy this formula. Second is the value of Lambda or arrival rate. So I'm going to put a value of two here, which for example, represents two customers a minute or an hour, whatever you want to provide. And then the third is whether you want to get a cumulative distribution or not. So whether you're talking about PDF or CDF, since we are interested in PDF, or just the probability value at or around this particular value of 0.1 in A2. I'm going to say 0. We're then going to copy this. Control R or Command R if you're using Mac. And this probability now is CDF or to convert it to CDF, the third parameter value in the formula we change from 0 to one. So now we have a cumulative probability distribution. You can fill it down. Control D or Command D depending upon the type of machine you're using. So here you see the probability distribution values both for individual values or the values-- Again, remember CDF represents the probability that a value equal to or less than that value occur. So in this case, 0.2. anything 0.2 or less. So now let's again see the shape of these curves. So just like we did last time, Let's try to create a graph. So I'm going to insert an XY type of graph. And here we see the value of -- Here we can see the pdf value, as you can see, high likelihood of small values occurring. What this reflects is that if the arrival rate is two, the values that most likely occur are 0.5 or less. There is some probability at 0.1. When you are arriving at around two, the probability becomes very, very small. Again, these are probabilities of the value of inter arrival times. That is, what is the time difference between two successive arrivals? If we, on the other hand, want to see the shape of CDF curve, it is slightly different from normal distribution. So again, if I insert an XY chart, we can see that instead of having an S type of curve now, we have an rapidly increasing probability and then it flattens out. So it's just kind of a reverse of that pdf function. Now, in case of normal distribution, while it is difficult to specify a specific function, there is a function but it's not easily calculable. In case of exponential distribution, we can also easily calculate these probabilities by using a formula. And that formula is right here. So for PDF, we can say probability of X is lambda, where lambda is your arrival rate multiplied by e to the power minus lambda x X is the parameter value that we are trying to calculate. So if I was going to calculate it, you can also simply calculate it like this, lambda which is two multiplied by e, which is the exponential function EXP. And it takes the parameter minus Lambda x, so minus two multiplied by this value of x. So if I calculate it this way, I get exactly the same value as I get using the exponential distribution function. So this, in this particular case, you might want to use the formula directly or you can calculate it using in Excel, this particular function. That's all we wanted to cover in this particular video. In the next few videos, we'll start applying these into our modeling framework and try to do our first larger scale simulation.