Question 1) Assume that the probability of rain tomorrow is 0.4 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.8 if it is clear today. Also assume that these probabilities do not change if information is also provided about the weather before today. a) Formulate the evolution of the weather as a Markov chain by defining its states and giving its (one-step) transition matrix. b) Draw the state transition diagram for this chain. c) Calculate the probability that it will rain three days from today given that it is raining today.

Question 1) Assume that the probability of rain tomorrow is 0.4 if it is raining today, and assume that the probability of its being clear (no rain) tomorrow is 0.8 if it is clear today. Also assume that these probabilities do not change if information is also provided about the weather before today. a) Formulate the evolution of the weather as a Markov chain by defining its states and giving its (one-step) transition matrix. b) Draw the state transition diagram for this chain. c) Calculate the probability that it will rain three days from today given that it is raining today.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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