3. (a) A Markov process with 2 states is used to model the weather in a certain town.State 1 corresponds to a suny day.State 2 corresponds to a rainy day.The transition matrix for this Markov process is[0.7 0.4]0.3 0.6%3D(i) If today is rainy, what is the probability that tomorrow will be sunny?(ii) Find the steady state probability vector.(iii) In the long run, how many days a week are sunny?

Part (i) Th transition matrix for the Markov process is, P=0.70.40.30.6 Given that today is rainy,…

3. (a) A Markov process with 2 states is used to model the weather in a certain town. State 1 corresponds to a sunny day. State 2 corresponds to a rainy day. The transition matrix for this Markov process is [0.7 0.4] P = 0.3 0.6 %3D (i) If today is rainy, what is the probability that tomorrow will be sunny? (ii) Find the steady state probability vector. (iii) In the long run, how many days a week are sunny?

3. (a) A Markov process with 2 states is used to model the weather in a certain town. State 1 corresponds to a sunny day. State 2 corresponds to a rainy day. The transition matrix for this Markov process is [0.7 0.4] P = 0.3 0.6 %3D (i) If today is rainy, what is the probability that tomorrow will be sunny? (ii) Find the steady state probability vector. (iii) In the long run, how many days a week are sunny?

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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