【正文】 s fit a line through the pointthe scatter of pointsand that39。t put down a name of a pany because I can39。s very unlikely that it39。s the correlation coefficient. That has kind of almost entered the English language in the sense that you39。s very basic here is covariance. Covariance is a measure of how much two variables move together. Covariance iswe39。s squared. It weights big deviations a lot because the square of a big number is really big. So, that39。s just the summation i = 1 to n of (x x bar)amp。micro。s often represented by σamp。s good. I would add up 20% a year for nine years and than put in a zero–no, 120 because it39。ve been investing money over a number of different years. Let39。s often reference to another kind of average, which I want to refer you to and which, in the Jeremy Siegel book, a lot is made of this. The other kind of average is called the geometric average. We39。s an infinite number of possibilities. We have instead what39。s an integral. We have the integral from minus infinity to plus infinity of F(x)*x*dx, and that39。re accountable and we can list all possible values when they39。ve just defined a random variable. You have discrete random variables, like the one I just defined, or there are alsowhich take on only a finite number of valuesand we have continuous random variables that can take on any number of values along a continuum. Another experiment would be to mix two chemicals together and put a thermometer in and measure the temperature. That39。s given by the formula where P is the probability of the accident: . That is the formula that insurance panies use when they have independent probabilities, to estimate the likelihood of having a certain number of accidents. They39。s not going to burn any other houses down since it39。t influence the second, we say they39。ll use the symbol P or I can sometimes write it out as prob to represent a probability. It is always a number that lies between zero and one, or between 0% and 100%. Percent means divided by 100 in Latin, so 100% is one. If the probability is zero that means the event can39。s just some intuitive sense that I canI don39。s why I think theory is very important in finance. Some people date fire insurance with the fire of London in 1666. The whole city burned down, practically, in a terrible fire and fire insurance started to proliferate right after that in London. But you know, you kind of wonder if that39。s because they didn39。t have a way to be rigorous. So, it was in the 1600s that probability theory started to get written down as a theory and many things then happened in that century that, I think, are precursors both to finance and insurance. One was in the 1600s when people started constructing life tables. What is a life table? It39。s theory. You don39。s a long story in the Mahabarahta about an emperor called Nala and he had a wife named Damayanti and he was a very pure and very good person. There was an evil demon called Kali who hated Nala and wanted to bring his downfall, so he had to find a weakness of Nala. He found finally some, even though Nala was so pure and so perfecthe found one weakness and that was gambling. Nala couldn39。m asking for an answer. It sounds like people have no idea. Can anyone venture a guess? No one wants to venture a guess? Student: fertile?Professor Robert Shiller: That he can father children? I don39。s lecturethen you should have no problem. I want to start with the concept of probability. Do you know what a probability is? We attach a probability to an event. What is the probability that the stock market will go up this year? I would saymy personal probability is .45. That39。s lecture is: The Universal Principle of Risk Management, Pooling and the Hedging of Risk. What I39。s a little rusty in his math skillsif he should take this course. I said, Well if you can understand tomorrow39。t always been that way and that probability is really a concept that arose in the 1600s. Before that, nobody ever said that. Ian Hacking, who wrote a history of probability theory, searched through world literature for any reference to a probability and could find none anywhere before 1600. There was an intellectual leap that occurred in the seventeenth century and it became very fashionable to talk in terms of probabilities. It spread throughout the worldthe idea of quoting probabilities. But it wasIt39。t publish it, and it never became part of the established literature partly because, he said, throughout human history, there has been a love of gambling and probability theory is extremely useful if you are a gambler. Hacking believes that there were many gambling theorists who invented probability theory at various times in history but never wrote it down and kept it as a secret. He gives an exampleI like tohe gives an example from a book thator it39。s a terrible storyand Nala then had to leave the kingdom and his wife. They wandered for years. He separated from her because of dire necessity. They were wandering in the forests and he was in despair, having lost everything. But then he meets someone by the name ofwe have Nala and he meets this man, Rituparna, and this is where a probability theory apparently es in. Rituparna tells Nala that he knows the science of gambling and he will teach it to Nala, but that it has to be done by whispering it in his ear because it39。s the ending. Anyway, that shows that I think probability theory does have a long history, butit not being an intellectual disciplineit didn39。 but you might think, but why just for burial? Why don39。tthey were intuitively halfway there but they couldn39。t have a clear meaning. It has been shown that even today people seem to think that. They don39。m lucky or this is my lucky day. Probability theory is really a movement away from that. We then have a mathematically rigorous discipline. Now, I39。s the basic idea. One of the first principles of probability is the idea of independence. The idea is that probability measures t