【正文】 He found finally some, even though Nala was so pure and so perfecthe found one weakness and that was gambling. Nala couldn39。 so the evil demon seduced him into gambling aggressively. You know sometimes when you39。ve lost? In a fit of gambling, Nala finally gambled his entire kingdom and lostit39。s a deep and extreme secret. Nala is skeptical. How does Rituparna know how to gamble? So Rituparna tries to prove to him his abilities and he says, see that tree there, I can estimate how many 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。s theory. You don39。 so he puts her and gambles her. But remember, now he knows what he39。t gambling his wifehe was really a very pure and honorable man. So he won back the entire kingdom and that39。t really inform a generation of finance theory. When you don39。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 what you need to know if you39。s an interesting concept. They were selling that in ancient Rome。t you make it into fullblown life insurance? You kind of wonder why they didn39。s because they didn39。s in the Journal of Risk and Insuranceand they translate a Renaissance insurance policy and it39。t have our language, they didn39。t express it, so I think the industry didn39。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。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 clearly have that in their mind from an intuitive standpoint. They have maybe a sense that I can influence events by willing or wishing and if I think thatif I have kind of a mystical side to me, then probabilities don39。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 typically bet more if they can toss the coin or they will bet more if the coin hasn39。s just some intuitive sense that I canI don39。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。t know what that meanslike God or the gods favor me and so I39。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。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 certain to happen. If the probability isCan everyone see this from over there? I can probably move this or can39。re the most disadvantaged person and you can see it, right? So that39。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。t influence the second, we say they39。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。re not independent. The theory of insurance is that ideally an insurance pany wants to insure independent events. Ideally, life insurance is insuring peopleor fire insurance is insuring peopleagainst independent events。s not the fire of London. It39。s not going to burn any other houses down since it39。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。s called the binomial distribution. I39。re insuring against an accident, then the probability that you39。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。m not going to expand on this because I can39。m hopeful that you can see the formula and you can apply it. Any questions? Is this clear enough? Can you read my handwriting? Another important concept in probability theory that we will use a lot is expected value, the mean, or averagethose are all roughly interchangeable concepts. We have expected value, mean or average. We can define it in a couple of different ways depending on whether we39。 I will call the oute heads the number one, and I39。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 continuous, right? When you mix two chemicals together, it could be any number, there39。micro。s the Greek letter muas the summat