Suppose that the weather in NYC is either sunny (S), rainy (R), or cloudy (C) (with no rain). By looking up back issues of the New York Times, we estimate that if it is sunny on a day, it is equally likely to be sunny or cloudy on the next day, and it will be rainy with 15 percent probability. if it is rainy on a day, it is equally likely to be rainy or cloudy on the next day, and it will be sunny with 20 percent probability. if a day is cloudy it is going to be sunny, rainy or cloudy with equal proba- bilities. We would like to model the evolution of weather using Markov chains as we did in class. Using the given information above answer the following questions: a) Write down carefully the state vector and transition matrix for the corre- sponding Markov system. b) Suppose that a day is cloudy, find the probabilities that the next day is going to be sunny, rainy, or cloudy. c) Suppose that a day is cloudy, find the probabilities that two days from that day is going to be sunny, rainy, or cloudy. d) Suppose day the weather forecast says tomorrow it will be S, R, and C with probabilities 0.6, 0.1, 0.3. Find the weather probabilities for the next two days after tomorrow. e) Does this system have a stationary distribution?

Suppose that the weather in NYC is either sunny (S), rainy (R), or cloudy (C) (with no rain). By looking up back issues of the New York Times, we estimate that if it is sunny on a day, it is equally likely to be sunny or cloudy on the next day, and it will be rainy with 15 percent probability. if it is rainy on a day, it is equally likely to be rainy or cloudy on the next day, and it will be sunny with 20 percent probability. if a day is cloudy it is going to be sunny, rainy or cloudy with equal proba- bilities. We would like to model the evolution of weather using Markov chains as we did in class. Using the given information above answer the following questions: a) Write down carefully the state vector and transition matrix for the corre- sponding Markov system. b) Suppose that a day is cloudy, find the probabilities that the next day is going to be sunny, rainy, or cloudy. c) Suppose that a day is cloudy, find the probabilities that two days from that day is going to be sunny, rainy, or cloudy. d) Suppose day the weather forecast says tomorrow it will be S, R, and C with probabilities 0.6, 0.1, 0.3. Find the weather probabilities for the next two days after tomorrow. e) Does this system have a stationary distribution?

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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