[1] Consider the Sunny-Rainy example we covered in class but suppose that the tran- sition matrix is given by the following matrix instead [0.8 0.2] P = 0.5 0.5 a) Suppose that at some time t, the weather is S or R with equal probability. Write down the state vector Tt and then compute t+1 and 7t+2, i.e. compute the probabilities that the weather will be S or R in t + 1 and t + 2. b) Suppose that at some time t, the weather is twice more likely to be Sunny than Rainy. Write down the state vector Tt, and then compute 7+1 and Tt+2. c) Find the stationary distribution corresponding to the transition matrix given above using the equation that defines stationarity. d) Suppose that at some time t, the weather is Sunny with probability 5/7. Compute the state vector for time t + 1 and t + 2. Did you expect these results? Explain your answer.
[1] Consider the Sunny-Rainy example we covered in class but suppose that the tran- sition matrix is given by the following matrix instead [0.8 0.2] P = 0.5 0.5 a) Suppose that at some time t, the weather is S or R with equal probability. Write down the state vector Tt and then compute t+1 and 7t+2, i.e. compute the probabilities that the weather will be S or R in t + 1 and t + 2. b) Suppose that at some time t, the weather is twice more likely to be Sunny than Rainy. Write down the state vector Tt, and then compute 7+1 and Tt+2. c) Find the stationary distribution corresponding to the transition matrix given above using the equation that defines stationarity. d) Suppose that at some time t, the weather is Sunny with probability 5/7. Compute the state vector for time t + 1 and t + 2. Did you expect these results? Explain your answer.
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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Show full answers and steps to this exercise. Please explain how you get to the answers without using excel, stata or R
![[1] Consider the Sunny-Rainy example we covered in class but suppose that the tran-
sition matrix is given by the following matrix instead
P =
[0.8 0.2
0.5
a) Suppose that at some time t, the weather is S or R with equal probability.
Write down the state vector πt and then compute t+1 and 7t+2, i.e. compute
the probabilities that the weather will be S or R in t + 1 and t + 2.
b) Suppose that at some time t, the weather is twice more likely to be Sunny
than Rainy. Write down the state vector , and then compute 7+1 and 7t+2.
c) Find the stationary distribution corresponding to the transition matrix given
above using the equation that defines stationarity
d) Suppose that at some time t, the weather is Sunny with probability 5/7.
Compute the state vector for time t + 1 and t + 2. Did you expect these
results? Explain your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3574180-5be7-46af-9f18-c1fbb9ec682c%2Fe3a7e134-341f-433f-84e3-2ac7051ef7a2%2F4chm6mh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[1] Consider the Sunny-Rainy example we covered in class but suppose that the tran-
sition matrix is given by the following matrix instead
P =
[0.8 0.2
0.5
a) Suppose that at some time t, the weather is S or R with equal probability.
Write down the state vector πt and then compute t+1 and 7t+2, i.e. compute
the probabilities that the weather will be S or R in t + 1 and t + 2.
b) Suppose that at some time t, the weather is twice more likely to be Sunny
than Rainy. Write down the state vector , and then compute 7+1 and 7t+2.
c) Find the stationary distribution corresponding to the transition matrix given
above using the equation that defines stationarity
d) Suppose that at some time t, the weather is Sunny with probability 5/7.
Compute the state vector for time t + 1 and t + 2. Did you expect these
results? Explain your answer.
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VIEWStep 2: Write state vector and compute probabilites for t+1 and t+2 when S and R are equally likely
VIEWStep 3: Write state vector and compute probabilites for t+1 and t+2 when S is two times more likely than R
VIEWStep 4: Find the stationary distribution
VIEWStep 5: Compute probabilities for t+1 and t+2 when S is 5/7
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