 Hi, this is Dr. Don. I have a problem out of Chapter 5, Section Point 2, which can be difficult and time-consuming to do, especially if you follow the procedure that they give you and show me an example or help me solve this, the manual method. But there's some ways you can do it faster, and I'll show you those. We'll do it using Excel because StatCrunch doesn't really have a tool that's set up to do this as easily as Excel. I'm going to click on the icon to view the table, and they give us really three tables here, the probability distribution of X, the probability distribution of the mean of the sample X bar, and then the full data set. And don't get distracted by this summary here. This is not what you'll get if you open up the full data set. So let's open that spreadsheet first. Click the open the table, open in Excel. It drops down to the bottom. I'm going to click to open that. I'm going to click done for right now. We can go back and get those other two spreadsheets when we're ready. You need to click on enable editing, and of course save that to your local hard drive. This is the way the data comes up. If you remember, they said that we observed the variable X two times. So here's observation one, observation two, and then the values they got. And of course, then they go ahead and calculate the mean between those two values and give you the probability that they recorded for those sets of observations. So now let's go ahead and find, first of all, the variance of the two observations. It's really straightforward to do. I'm going to label this column variance, which is also S squared. And all I'm going to do is to use the function equal var, and we start getting offerings there. We want the variance of samples because these are samples, not the entire population. So I'm going to double click that to select it. And then we want our two numbers, our two observations, range one, range two, and hit enter. So that's our variance for that first set of two observations. And now I can just drag that down to get the variances for all of the observations. Now, one of the things I like to do in order to make sense of this, if I can go a little easier, I'm going to leave that column selected and then go to data. And then I'm going to sort it from smallest to largest. It'll say expand this section. I'm going to say yes. So now I've got it sorted, so it's a little easier to make sense of. If you call the problem said, type the answers and ascending orders for the variance. And that's what I've done when I reordered that. So these are our variances in our samples, 0, 5, 2, 4.5, and 8. So how do I get the probabilities of getting each of those variances? Well, it's pretty simple. I'm going to label this P of variance. And it is just equal to the sum of the probabilities for each one of those zero variances. And so I get that answer there, a 0.22 is my first point in my variance probability distribution. I go down here again, equal issue sum and sum of the probabilities for all the variances that are 0.5 and that column right there. And then we'll do the same thing down here for 2. There's my probabilities for a variance of 2. Probabilities for variance of 4.5. And then my probabilities of the variances of 8. So those are my values. The distribution is 0.22, 0.5, 0.32, 2.22, 4.5 variance, 0.16, variance of 8, 0.08. And those are the answers there. I'll show you part B in the next video.