28. Suppose that whether it rains in Charlotte tomorrow depends on the weather conditions for today and yesterday. Climate data from 2003 show that • If it rained yesterday and today, then it will rain tomorrow with probability 58. • If it rained yesterday but not today, then it will rain tomorrow with probability .29. If it rained today but not yesterday, then it will rain tomorrow with probability 47. • If it did not rain yesterday or today, then it will rain tomorrow with probability 31. Even though the weather depends on the last two days in this case, we can create a Markov chain model using the states 1 itrained yesterday and today 2 it rained yesterday but not today 3 it rained today but not yesterday 4 it did not rain yesterday or today So, for example, the probability of a transition from state I to state I is .58, and the transition from state I to state 3 is 0.

28. Suppose that whether it rains in Charlotte tomorrow depends on the weather conditions for today and yesterday. Climate data from 2003 show that • If it rained yesterday and today, then it will rain tomorrow with probability 58. • If it rained yesterday but not today, then it will rain tomorrow with probability .29. If it rained today but not yesterday, then it will rain tomorrow with probability 47. • If it did not rain yesterday or today, then it will rain tomorrow with probability 31. Even though the weather depends on the last two days in this case, we can create a Markov chain model using the states 1 itrained yesterday and today 2 it rained yesterday but not today 3 it rained today but not yesterday 4 it did not rain yesterday or today So, for example, the probability of a transition from state I to state I is .58, and the transition from state I to state 3 is 0.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

QUESTION : Suppose that the weather in Charlotte is modeled using the Markov chain in THE ATTACHED PICTURE. About how many days elapse in Charlotte between consecutive rainy days?

28. Suppose that whether it rains in Charlotte tomorrow depends
on the weather conditions for today and yesterday. Climate
data from 2003 show that
• If it rained yesterday and today, then it will rain
tomorrow with probability 58.
• If it rained yesterday but not today, then it will rain
tomorrow with probability 29.
• If it rained today but not yesterday, then it will rain
tomorrow with probability 47.
• If it did not rain yesterday or today, then it will rain
tomorrow with probability 31.
Even though the weather depends on the last two days in this
case, we can create a Markov chain model using the states
1 it rained yesterday and today
2 it rained yesterday but not today
3 it rained today but not yesterday
4 it did not rain yesterday or today
So, for example, the probability of a transition from state I to
state 1 is .58, and the transition from state I to state 3 is 0.

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