Foundations of Stochastic Processes 048868 Due 09:00, July 19, either by hand to Meir 1233 or electronically to Summary: Foundations of Stochastic Processes ­ 048868 Final Exam Due 09:00, July 19, either by hand to Meir 1233 or electronically to robert@ee.technion.ac.il The exam might seem long, but, in the unforgettable words of The Hitch- hiker's Guide to the Galaxy, DON'T PANIC! The reason each question is so long is that I broke it into small pieces so that if there is one step that you cannot do you can still go on from there to the next one. Question 1: My home is equidistant to a cake shop and a chocolate shop, and each day I choose, at random, to go to one of these shops to buy either a cake or a chocolate for breakfast. On the first day, I have no preference for either shop, and so choose between them with equal probabilities. However, both the cakes and the chocolates are very tasty, and so the positive reinforcement I get from my choice affects my probabilities for later days, in the following fashion: Let Nn be the number of times that I have visited the cake shop after n days. Then, given the entire history of the process up to and including day n, the probability of choosing the cake shop on day n + 1 is Collections: Mathematics; Engineering