So many congratulations for making it through week 1. So let's just perhaps consider some of our key takeaways from the first few sessions of this course. So our main point is that I want you to recognize that we live in a highly complex and uncertain world. Whether you like uncertainty or dislike it, it's a fact of life and we have to deal with it. So our goal is to make well-informed decisions and have to make those decisions under uncertainty. So it's not an ideal situation but indeed we don't live in an ideal world. We live in this real world of uncertainty. So the best we can do is to try and quantify the uncertainty and take optimal decisions based on what we know at a given point in time. Now, I think this was very well illustrated in our introductory game of that Monty Hall problem, whereby what we were really solving for is not probabilities per say but a strategy. What was the right thing to do? Well, from a probabilistic perspective the optimal strategy is to always switch to the other door each time. By doing so, you are maximizing your chance of success. Whereby in that game you would have a two thirds probability of winning the sports car. True, in this play of the game, you are unlucky but of course we shouldn't be concerned with just a one shot game versus a multi shot game, whereby we do things many, many times and we recognize whether chance, luck; good luck, bad luck exists and we are all prone to experiencing both good and bad luck. But if we play things optimally, probabilistically then we will tend to win far more often than we lose. We've also introduced the concept of a model. Our way of trying to describe some aspect of the real world whereby this model should be a deliberate simplification of reality. Of course, the challenge is to decide what are the most important, the most salient features of the real world which should feature in our model and which things are less important and could be discarded. We gave the London Underground map as an excellent example of an attempt to deliberately simplify the real world. I'll leave it to your own judgment from the famous Underground map from the geographically accurate one both being models but which one did you feel was the better model. Ultimately, that's down to our own opinion and judgment. But do appreciate the trade-offs which we face, being geographically accurate and in one case and perhaps being easier to interpret map in the other case and think about the trade-offs involved. We've also considered uncertainty in the news and please do going forward listen out to that word uncertainty when it's mentioned by a reporter. When you hear about interest rates being raised or decreased, when you hear the latest inflation figures being reported, when you hear about volatile movements in the financial markets, think of this as being the markets reacting to new information. Indeed, when things do change, how does it compare to our expectations? Are things as we had expected or do they differ from our expectations and hence should there be any revisions to our beliefs about the world that say you from a probabilistic perspective and what consequences could this have for decision making? Also, we touched on briefly the importance of assumptions in model building. Yes, we introduce assumptions primarily to simplify the real world which is a desirable goal. However, please be aware of the pitfalls of making flawed assumptions because any inferences or conclusions we draw from models could be severely affected by our choice of assumptions and may lead us to doing something which leads to a very bad outcome in the end. So those are really our key takeaways from week 1. So we kept it out at a fairly light level, the sort of calculations and theory bits to come later on. But hopefully this has given you a nice introduction into how we have to deal with the uncertainty that we all face on a daily basis.