Exercise instructions 2.1 Weather Markov Prerequisite: Slide 2.30 (1) The simple Markov chain model of the weather had only two states "Sunny" and "Rainy"; add a third state "Cloudy". The transition...

Exercise instructions 2.1 Weather Markov

Prerequisite: Slide 2.30 (1) The simple Markov chain model of the weather had only two states "Sunny" and "Rainy"; add a third state "Cloudy". The transition probabilites are: Sunny > Sunny 0.7, Sunny > Rainy 0.2, Sunny > Cloudy 0.1; Rainy > Sunny 0.4, Rainy > Rainy 0.4, Rainy > Cloudy 0.2; Cloudy > Sunny 0.3, Cloudy > Rainy 0.3, Cloudy > Cloudy 0.4. Implement the transition matrix for this three-state weather model. (2) Use the three-state weather model and matrix multiplication to calculate the probabilies for each state on days 2 - 5. Assume that the weather is Sunny on day 1.

PowerPoint Presentation Model Types and Modeling Methods 2.30 Simple model for tomorrow’s weather, based on today’s Supports calculation future days’ weather probabilities S1Sunny S2Rainy Example Markov chain Weather prediction Markov chain 0.90.5 S1 S2 0.1 0.5 Weather day 0 sunny x (0)  10 Predicted weather day 1 x (1)  x (0) P  10  0.90.1 Predicted weather day 2 x (2)  x (1) P  0.90.1   0.86 0.14 Predicted weather day n x (n)  x (n 1) P  x (0) Pn 0.90.1 Transition matrix P   0.50.5 0.5 0.5 0.1 0.9 0.90.1  0.5 0.5