【正文】 ell, nothing in terms of the math. The probability theory is new. Others though, I want to tell you that it doesn39。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 what she meant but maybe. No, what apparently she meant is trustworthy. That39。 so the evil demon seduced him into gambling aggressively. You know sometimes when you39。 so he puts her and gambles her. But remember, now he knows what he39。s what you need to know if you39。s in the Journal of Risk and Insuranceand they translate a Renaissance insurance policy and it39。re also going to recognize, however, that insurance got a slow start becauseI believe it is becausepeople could not understand the concept of probability. They didn39。t change things, there are all these objective laws of probability out there that guide everything. Most languages around the world have a different word for luck and riskor luck and fortune. Luck seems to mean something about you: like I39。s certain to happen. If the probability isCan everyone see this from over there? I can probably move this or can39。s no relation between the two. One of the first principles of probability theory is called the multiplication rule. That says that if you have independent probabilities, then the probability of two events is equal to the product of their probabilities. So, the Prob(A and B) = Prob(A)*Prob(B). That wouldn39。t back when the idea first came up. Incidentally, we have a problem set, which I want you to start today and it will be due not in a week this time, because we have Martin Luther King Day ing up, but it will be due the Monday following that. If you follow through from the independent theory, there39。m not going to expand on this because I can39。s continuous, right? When you mix two chemicals together, it could be any number, there39。s called the expected value. People also call that the mean or the average. But, note that this is based on theory. These are probabilities. In order to pute using this formula you have to know the true probabilities. There39。s the same thing because an integral is analogous to a summation. Those are the two population definitions. F(x) is the continuous probability distribution for x. That39。re not going to need to know a lot about this for this course, but this isI wanted to get the basic ideas down. These are called population measures because they refer to the whole population of possible outes and they measure the probabilities. It39。ll only show the sample version of it G(x) = the product i = 1 to n of (xi )^(1/n). Does everyoneCan you see that? Instead of summing them and dividing by M, I multiply them all together and take the nth root of them. This is called the geometric average and it39。s not a very good thing to do. What he says you should do instead is to take the geometric average of gross returns. The return on an investment is how much you made from the investment as a percent of the money invested. The gross return is the return plus one. The worst you can ever do investing is lose all of your investmentlose 100%. If we add one to the return, then you39。t look bad, right? But think about it, if you were investing your money with someone like that, what did you end up with? You ended up with nothing. If they have one year when they lose everything, it doesn39。, that39。s the expectation of x or also E(x), so it39。/n. That is the sample variance. Some people will divide by n–1. I suppose I would accept either answer. I39。re going to be talking about these in finance in regards to returns becausegenerally the idea here is that we want high returns. We want a high expected value of returns, but we don39。ll just talk about it in a sample term. It39。t know how much you39。t be negative. It couldn39。s not say Microsoft, let39。s called the regression line and the intercept is called alphathere39。re often negative. Suppose that in a given yearand say this is minus five and this is plus five, this is minus five and this is plus fiveSuppose that in the first year in our sample, the pany Shiller, Inc. and the market both did 5%. That puts a point right there at five and five. In another year, however, the stock market lost 5% and Shiller, Inc. lost 7%. We would have a point, say, down here at five and seven. This could be 1979, this could be 1980, and we keep adding points so we have a whole scatter of points. It39。s say Microsoft. I39。s way below one, but it has some correlation, so maybe it39。s a scaled covariance. We tend to use the Greek letter rho. If you were to use Excel, it would be correl or sometimes I say corr. That39。s uncertainty. That39。s a measure of how much x deviates from the mean。. There39。sup2。re advertising your return you want to make it look as big as possible. We also need some measure ofWe39。ve produced 20% a year for nine out of the last ten years. You think that39。s an appendix to one of the chapters in Jeremy Siegel39。m having a little trouble putting this into the Rituparna story, but you see the idea. You know the average, I assume. That39。 is zero because it could be 176。micro。s the Greek letter muas the summation i = 1 to infinity of. [P(x=xi) times (xi)]. I have it down that there might be an infinite number of possible values for the random variable x. In the case of the coin toss, there are only two, but I39。 I will call the oute heads the number one, and I39。re insuring against an accident, then the probability that you39。s not the fire of London. It39。s say the oute of an experiment, like tossing a coin. You might say the probability that you toss a coin and it es up heads is a half, because it39。m going to go through some of the terms of probability andthis will be review for many of you, but it will be something that we39。t really take, at an intuitive level, probabilities as objective. For example, if you ask people how much they would be willing to bet on a coin toss, they will typicall