Open course ware

PROFESSOR: There are several mediums of working with students in the process of designing. There are desk-side crits. There are reviews. There are lectures. And there are pinups. In this studio, every week, a piece of the project is due, whether it be a model or a drawing. And we have what we call pin up, when all the students pin up their work and quickly explain what they are doing. And then I and other members of the class try to give comments on what they've seen to try to help to the next step. Because architecture is not just one step. It's a continual process that changes. Perhaps people have the idea that it comes all at once. It doesn't. It comes over a period of time. So the pin up is a very valuable part of that. Because it's giving students a feedback as to how they're moving. And slowly, adjustments are made for the next step. So what you're about to see is a typical pin up of which happens almost every week during the semester. STUDEN...

We have seen that several properties, such as, for example, linearity of expectations, are common for discrete and continuous random variables. For this reason, it would be nice to have a way of talking about the distribution of all kinds of random variables without having to keep making a distinction between the different types-- discrete or continuous. This leads us to describe the distribution of a random variable in a new way, in terms of a so-called cumulative distribution function or CDF for short. A CDF is defined as follows. The CDF is a function of a single argument, which we denote by little x in this case. And it gives us the probability that the random variable takes a value less than or equal to this particular little x. We will always use uppercase Fs to indicate CDFs. And we will always have some subscripts that indicate which random variable we're talking about. The beauty of the CDF is that it just involves a probability-- a concept that is well defin...