Hello, and a very warm welcome to the Smoke called Probability and Statistics: To P or not to P. I'm Dr. James Abdey our lecturer in statistics. And, I'd like you to join me on this voyage of discovery where we're going to introduce some fundamental concepts related to probability and statistics. Now, I'm guessing you're wondering what the to P or not to P is all about. Well, if I tell you that the P represents probability, we are posing a binary question of whether we should take a probabilistic approach to decision making or whether we shouldn't. Well, I'm biased but I like to think I'm right in that we should take a probabilistic approach to decision making. Why? Well, decision making, we have to make decisions in the present but there are unknown and uncertain future outcomes. So, whether you like uncertainty or not, we're stuck with it. The bad side about uncertainty is that it's a real pain for decision making because we don't know for sure what's going to happen. The flip side is that at least uncertainty makes life interesting. It makes it exciting because there's the uncertainty of the future. Imagine the whole of the rest of your life was completely known. Maybe you are destined for a good future. Maybe a bad future. Maybe a mediocre future. But, the point is, it would be a known future and there would never be any element of surprise. So, we do live with uncertainty. And probability and statistics will allow us to quantify uncertainty and hopefully assist us in our decision making. So, what are you going to take away from this smoke? Well hopefully, a variety of things. We're going to consider some theoretical concepts. For example, derive some simple probability distributions. Consider the shape of a probability distribution itself. Focus on key attributes of a distribution such as the mean and the variance, which are two very fundamental components of statistics which allow us to form many decisions. And, we'll go beyond that and delve into the world of statistical inference. Point estimation. Estimating parameters, turning into confidence intervals. Reflecting the uncertainty when we estimate some particular characteristic. We'll also delve into hypothesis testing. Imagine, someone comes up with a theory or a claim about something. Should we believe it or not? Well, we want to look for evidence either to support or refute said theory or claim. And, in the final week of this smoke, I'm going to offer you a selection of useful applications or various quantitative methods, for solving different problems. We return to that decision making under uncertainty and we could model that, for example, using decision trees. We also want to consider more formally the concept of risks. So, we will investigate how we can determine someone's risk profile and hence their attitude towards risk. And, we may consider some simple financial applications. For example, the riskiness of a stock. We'll briefly touch on linear regression analysis, one of the most widely used statistical techniques out there. And, we will make some links and connections with material covered previously, earlier in the course. And we will round off with a look Monte-Carlo simulation. Which really will bring us full circle back to our initial problem of decision making under uncertainty. A very useful technique for coming up with an expectation of what may happen if we undertake a project, but very importantly, the quantification of risk as well. So, I very much look forward to sharing my joy and love of statistics with you as we embark on this smoke.
