Showing posts with label probability. Show all posts
Showing posts with label probability. Show all posts

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! 


NOW USING CHROME

Reading Update:
The Drunkards Walk by Leonard Mlodinow









I am up to chapter three and I have learned very little and read a twenty page review of the first quarter of a statistics class I took. Here are the first two chapters in summary.

Chapter 1:
  • The right side of your brain is 'intuitive' and always tries to find heuristics
  • The left side of your brain is 'logical' and always tries to find patterns
  • If two events are occuring randomly and event 1 occurs thrice as much as event 2, in guessing which event will occur next, you will be correct more often if you simply choose the event that occurs more often everytime.
  • Praising a person for good behavior is more effective than punishing people for bad behavior
  • This can seem counter intuitive due to regression toward the mean; that is, after someone does much better than they usually do, it is natural for them to do about as well as they had been doing before that accidental success, the same goes for accidental mistakes.
Chapter 2:
  • This is a review of probability rules
  • The probability that two events will occur can never be greater than the probability that each event will occur individually
  • You can predict the probability that two events will occur by taking the product of the probabilities of the two events ONLY IF the two events are completely independent of each other.
  • The probability that, given an event with multiple different and possible outcomes, the probability that one outcome or another outcome will be the result is the sum of the probabilities of two potential outcomes (assuming that the sum of all of the possible outcomes is 1 [100%])
  • When making a point about the potential outcomes of an event, make sure you are looking at the correct proability.