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Unformatted text preview: Massachusetts Institute of Technology Department of Electrical Engineering & Computer Science 6.041/6.431: Probabilistic Systems Analysis (Fall 2010) Problem Set 2 Due September 22, 2010 1. Most mornings, Victor checks the weather report before deciding whether to carry an umbrella. If the forecast is rain, the probability of actually having rain that day is 80%. On the other hand, if the forecast is no rain, the probability of it actually raining is equal to 10%. During fall and winter the forecast is rain 70% of the time and during summer and spring it is 20%. (a) One day, Victor missed the forecast and it rained. What is the probability that the forecast was rain if it was during the winter? What is the probability that the forecast was rain if it was during the summer? (b) The probability of Victor missing the morning forecast is equal to 0.2 on any day in the year. If he misses the forecast, Victor will ip a fair coin to decide whether to carry an umbrella. On any day of a given season he sees the forecast, if it says rain he will always carry an umbrella, and if it says no rain, he will not carry an umbrella. Are the events Victor is carrying an umbrella, and The forecast is no rain independent? Does your answer depend on the season? (c) Victor is carrying an umbrella and it is not raining. What is the probability that he saw the forecast? Does it depend on the season?...
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- Fall '10
- Electrical Engineering