4. (5 points) Consider a two-state Markov chain. Suppose that we have two states of the weather: sunny or cloudy. If today is sunny, the probability of being sunny tomorrow is 3/4. If today is cloudy, the probability of being cloudy tomorrow is 1/2. Find the stable distribution for the Markov chain.
Added by John M.
Close
Step 1
Step 1:** Write down the transition matrix based on the information given in the problem: \[ P = \begin{pmatrix} 3/4 & 1/4 \\ 1/3 & 2/3 \end{pmatrix} \] ** Show more…
Show all steps
Your feedback will help us improve your experience
Zhaojie Xu and 98 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Suppose that whether or not it rains today depends on the weather conditions in the last three days. In particular, if it rained for the past three days, then it will rain today with probability 0.8; if it did not rain for any of the past three days, then it will rain today with probability 0.2; and in any other case, the weather today will, with probability 0.6, be the same as the weather yesterday. (a) Show that this system can be modeled by using a Markov chain. How would you define the states of the process? How many states are needed? (b) Write the transition probability matrix for this Markov Chain.
Samriddhi S.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD