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Unformatted text preview: CS 188 Final Exam, 58 pm, Wed Dec 16, 1998 1. In this problem, you are asked to model a simplified version of the weather and umbrella HMM, that we all know and love. The weather on any day can be either sunny or rainy, each with prior probability 0.5. From one day to the next, the weather remains the same with probability 0.8 and changes with probability 0.2. On a sunny day, the probability that you will observe the caretaker carrying an umbrella is 0.3, on a rainy day it is 0.7. The weather outside is hidden to you, all you can observe is the presence (or absence) of an umbrella. (a) If on the first day of your enforced seclusion, you observed the caretaker come in without an umbrella, what is the chance that the weather outside is raining? (b) Now suppose that you observe that on the second day, the caretaker came in with an umbrella. What would you now say about the probability that the weather out side was rainy on the first day?...
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 Spring '08
 Staff
 Computer Science, Probability distribution, Rain, Joint probability distribution, Soda Hall–its job, mail delivery robot

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