Reading Update:
Chapter 4
Chapter 4 is more exciting than the past three and, though it covers a few principals found in most elementary statistics classes, it brings in new characters to the story like Galileo and Pascal! Here goes:
- The simple space technique (using a space or coordinates to denote potential outcomes) can only be used when the outcomes are equally probable
- The chances of an event depend on the number of ways in which it can occur. This is important, so how do you calculate it?
- Pascal's Triangle
- Mathematical expectation = probability of each outcome * payoff of each respective outcome, i.e. the cost of something, say a parking meter, is the probability of each outcome ($40.00 ticket 1 out of 20 times I use one and $0.25 on the rest of the time [19 out of 20]) so $40*1/20 + $0.25 each time I use it = $2.25. So the real cost of paying a parking meter is about $2.25 each time I use one if I average it out.
- This idea has been helpful for winning lottery tickets. For example, if you calculate the expectation of buying all of the different combinations of six numbers from 1 to 44, and compare that with the payoff of about 27 million, you will find something quite interesting! There are 7,059,052 ways to choose those six numbers with a pot of that size, each ticket is worth almost $4. Now remember that it is possible for other people to win at the same time. Appropriate the probabilities of winning alone or with other people and add them all up to come to a grand total worth of $3.31. The price to buy one is $1. What is the appropriate course of action here? Hire a whole bunch of investors, fill out 1.4 million slips by hand (each with 5 games) and coordinate a massive ticket purchasing campaign. The result? 27 million dollars!
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