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The fire danger during the summer in Mount Baker National Forest is classified into one of three danger levels. These are 1 =low, 2 =moderate, 3 =high. The probability of daily transitions between these states is given by the following flow diagram:

(a) Write the model in matrix form to project the fire danger probability from one day to the next.

Image: https://i.stack.imgur.com/TRuUy.png

(b) If we are in State 1 today, what is the probability that we will be in State 2 the day after tomorrow?

(c) If the matrix you found is correct, then it has eigenvalues and eigenvectors given by

Lambda = [
1.0000     0         0
0          0.0697    0
0          0         0.4203

R=
-0.4699   -0.5551    -0.7801
-0.7832   0.7961     0.1813
-0.4072   -0.2410    0.5988

Based on these, what is the equilibrium probability of being in each state?

I found the matrix form for part a, I could not figure out part b and c. Thank you

  A = [0.5    0.3    0
     0.4    0.5    0.5
     0.1    0.2    0.5]
user1877120
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1 Answers1

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Calculate your eigenvectors and eigenvalues by putting matrix A into the box here: http://www.arndt-bruenner.de/mathe/scripts/engl_eigenwert2.htm

Forecasts for the 2nd day after today will be given by element (2,1) of the matrix B = ((A*A)*A).

Alptigin Jalayr
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