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Previously in Industrial Organization Professor Wagner was talking about stochastic processes. The simplest case, and the one we dealt with in class was a version of Polya’s Urn which is a neat mental exercise. Imagine a jar with a brown pebble and a white pebble in it. Close your eyes and pull a stone at random from the jar. If the pebble is brown put that pebble back and add another brown pebble. If the pebble is white put it back in and add another white pebble. Now the urn has 3 pebbles and your chances of pulling a brown pebble or a white pebble are no longer 50/50 they are either 33/66 or 66/33 depending on whether you pulled a brown pebble or a white pebble.
Put another way this means that your chance of pulling a white pebble on the second pull depend on what you pulled on the first pull. And that your chances of pulling a white pebble on the third pull depend on what you pulled for the second pull which depends on what you pulled on the first pull.
We covered this in the last twenty minutes of class on Thursday, and then very briefly at the beginning of class on Tuesday. We only really need to know the very basics for the test, and even needing to know that is debatable. However a friend of mine in the class and I were discussing the topic during our break and we started arguing about the statistical distribution of the model. Now after we went back into the class room, but before the professor started teaching again, I wrote a program to show the statistical distribution, and my friend did a mathematical model to do likewise. After class we argued this for around a half an hour, without either of us proving the other wrong. I then spent another hour redoing his math to see if he had a mistake. After that I spent another twenty minutes creating a recursive equation to calculate the probability of getting a result. I did all of this work for something that most likely not show up on the test and if it does will only be at most ten percent of the test. As much fun as this is I now have to stay up late catching up all the work I should have been doing instead of playing with fun math problems. Not my best week for time management.