[MUSIC] Well, hello everybody, and welcome to the third lecture of the Statistics for International Business MOOC. This week we will introduce to you the concept of probability and distributions. The material presented this week shows why we all should understand probability. As a financial trader and professor, Nassim Nicholas Taleb points out, probability is about luck disguised and perceived as skills, and more generally, randomness, disguised and perceived as non-randomness, that is determinism. More generally, we underestimate the share of randomness in about everything around us. Probability is a young arrival in mathematics. And probability applied to practice is almost nonexistent as a discipline. We seem to have evidence that what is called carriage comes from an underestimation of the share of randomness in things, rather than the more noble ability to stick one's neck out for a given belief. So this week we will focus understanding probability. This will allow us to be prepared and avoid some of the effects of what I mentioned earlier. However, we will also discuss why it is important to understand that not everything can be predicted. For example, natural disasters or sudden political events, may have a huge impact to business and economics. These unpredictable events have been called black swans. We begin our presentation of probability to represent events with uncertain outcomes. We begin to adopt these ideas, and thereby developed probability models. We begin with discrete random variables. And then we will present probability models that are adequate and appropriate for continuous random variables. Probability models are extensively adopted to solve a number of business problems. Many of these applications are developed during the week. Suppose, for example, that you own a business renting a variety of equipment. From past experience, you know that 45% of the buyers entering your store want to rent a certain type of device. You have three such devices available at the moment. Six unrelated people enter the store. And we note that the likelihood that one rents a particular device is independent of the probability that others will ask to rent the same kind of device. So we ask ourselves, what is the probability that these six people who have entered our store are seeking to rent a total of four or five devices? Now if that happens, we will have missed some profit opportunities. And of course our customers will not be happy. The probability of the events that is the number of devices that are desired by the clients, may be computed using a kind of model called the binomial model. The problem we've just presented is just an example of a situation where a probability may be computed using a standard probability model. These models simplify problem-solving and the calculation of probabilities. However, when we want to use such a standard model, some important assumptions must be satisfied. So we begin with some definitions. And then we move on to present several important models that are used extensively in business, financial, and economic applications. Finally, we generalize values of these concepts related to probability to continuous random variables. And we conclude by discussing probability distributions. Thank you. [MUSIC]