【正文】 any leaves there are on that tree by counting leaves on one branch. Rituparna looked at one branch and estimated the number of leaves on the tree, but Nala was skeptical. He stayed up all night and counted every leaf on the tree and it came very close to what Rituparna said。 so the evil demon seduced him into gambling aggressively. You know sometimes when you39。s a collectionI think, a collection of epic poems written in Sanskrit that goes backit was actually written over a course of 1,000 years and it was pleted in the fourth century. Well, there39。s what she meant but maybe. No, what apparently she meant is trustworthy. That39。s funny that such a simple idea hadn39。m a bear butDo you know what that means? That 45 times out of 100 the stock market will go up and the other 55 times out of 100 it will stay the same or go down. That39。s lecturethat39。s a little bit unfortunate that it es early in the semester. For those of you who have had a course in probability and statistics, there will be nothing new here. Well, nothing in terms of the math. The probability theory is new. Others though, I want to tell you that it doesn39。Lecture 2 The Universal Principle of Risk Management: Pooling and the Hedging of Risks Overview:Statistics and mathematics underlie the theories of finance. Probability Theory and various distribution types are important to understanding finance. Risk management, for instance, depends on tools such as variance, standard deviation, correlation, and regression analysis. Financial analysis methods such as present values and valuing streams of payments are fundamental to understanding the time value of money and have been in practice for centuries.Reading assignment:Jeremy Siegel, Stocks for the Long Run, chapter 1 and Appendix 2, p. 12Financial Markets: Lecture 2 Transcript January 16, 2008 Professor Robert Shiller: Today I want to spendThe title of today39。tif you39。s today39。s a probability. Now, you39。t been used before. Hacking points out that the word probabilityor probablewas already in the English language. In fact, Shakespeare used it, but what do you think it meant? He gives an example of a young woman, who was describing a man that she liked, and she said, I like him very much, I find him very probable. What do you think she means? Can someone answer that? Does anyone know Elizabethan English well enough to tell me? What is a probable young man? I39。s a very important quality in a person I suppose. So, if something is probable you mean that you can trust it and so probability means trustworthiness. You can see how they moved from that definition of probability to the current definition. But Ian Hacking, being a good historian, thought that someone must have had some concept of probability going before, even if they didn39。s a storythere39。re losing and you redouble and you keep hoping to win back what you39。 so hethe next morningbelieved Rituparna. Now this is interesting, Hacking says, because it shows that sampling theory was part of Nala39。s doing and so he really wasn39。t have a theory, then you don39。re going to do life insurance. So, they started to do collecting of data on mortality and they developed something called actuarial science, which is estimating the probability of people living. That then became the basis for insurance. Actually, insurance goes back to ancient Rome in some form. In ancient Rome they had something called burial insurance. You could buy a policy that protected you against your family not having the money to bury you if you died. In ancient culture people worried a great deal about being properly buried, so that39。t. I think maybe it39。s very hard to understand what this policy was saying. I guess they didn39。t get really started. I think it was the invention of probability theory that really started it and that39。t have the concept firmly in mind. There are lots of aspects to it. In order to understand probability, you have to take things as ing from a random event and people don39。t been tossed yet. It could have been already tossed and concealed. Why would that be? It might be that there39。m a lucky person. I don39。re going to use in theSo I39。t I? Yes, I can. Now, can you nowyou39。s equally likely to be heads and tails. Independent experiments are experiments that occur without relation to each other. If you toss a coin twice and the first experiment doesn39。t hold if they39。s the problem that sometimes people knock over an oil lamp in their home and they burn their own house down. It39。s one of the basic relations in probability theoryit39。ll get x accidents and n trials. The binomial distribution gives the probability as a function of x and it39。t get intoThis is not a course in probability theory but I39。ll call the oute tails the number zero, so I39。s an infinite number of possible numbers and that would be continuous. For discrete random variables, we can define the expected value, or amp。m saying in general there could be an infinite number. But they39。s another formula that applies for a continuous random variables and it39。x, except that it39。s different when you have continuous valuesyou don39。 or something else and there39。s the truth, but there are also sample means. When you getthis is Rituparna, counting the leaves on a treeyou can estimate, from a sample, the population expected values. The population mean is often written xbar. If you have a sample with n observations, it39。s the most elementary concept and you could use it to estimate either a discreet or continuous expected value. In finance, there39。s used only for positive numbers. So, if you have any negative numbers you39。s book where he says that one of the most important applications of this theory is to measure how successful an investor is. Suppose someone is managing money. Have they done well? If so, you would say, Well, they39。ve got a number that39。s great, but what about the last year. The guy says, Oh I lost 100% in that year. You might sa