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So, the main topic for the next couple lectures is continuous distributions. We've learned about the binomial, and the poisson, and the hypergeometric, and so on, and at this point we've covered all of the famous discreet distributions that we need in this course. And no now is a good time to start talking about the continuous distributions. I like to do discreet before continuous, because conceptually it's simpler to think about discreet. But it doesn't mean that continuous is harder, necessarily, because discreet is kind of conceptually easier in a sense. But, on the other hand, we have all these nasty sums that come up, and so we learn some ways to sometimes avoid the sums using stories, and so on, but sometimes you just have the sum you can't deal with. The continuous case, we'll be doing integrals instead of sums, and even though this sounds counterintuitive, in general, it's easier to do an integral than a sum. Although the same thing could come up, we could be faced with integrals we don't know how to do. So again, we're gonna try to look for kind of more clever, and more conceptual ways to avoid having to do lots and lots of integration. But anyway, we'll come to that later. But, a lot of the ideas are completely analogous. So, at this point, I'm assuming you have a pretty good understanding of what a PMF is, and what is a discreet distribution? What does it really mean, and the expected value of a discreet distribution, and now we're just gonna move into the continuous case. So, I think, and just for having a big picture on this, it helps to just kind of contrast the two things. So I'm gonna make kind of a dictionary of discrete world and continuous worlds. So we can put discrete world over here and continuous world over here. So we have a random variable that we're looking at, and usually we've been calling our random variable x in the discrete case, and usually we'll call it x in the continuous case. So, so far it's completely analogous. We got discrete, continuous. Now in the discrete case, as you're very familiar with by now, we have a PMF, Which you can just think of as the P(X=x), viewed as a function of little x. So if it takes positive integer values, then I would need to specify this for all positive integers x. In the continuous case, the [P(X=x)=0]. So in that case we have a PDF instead, which usually we would write as f(x), but you can call it whatever you want. I'll call it f sub x (x) just to emphasize that this is the PDF of x. So I'm gonna tell you what a PDF is, but I'm just telling you now, that it's analogous to a PMF. The reason we need this is that the [P(X=x)=0]. So continuous, it means we're thinking of random variables that could take on...