1. In Neverland, there are two political parties, Freedom Party (F) and Patriot
ID: 3039834 • Letter: 1
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1. In Neverland, there are two political parties, Freedom Party (F) and Patriot Party (P) During any given year, a Freedom Party member might switch to Patriot Party with probability 0.10, become an independent (I) with probability 0.15, or remain in Freedom Party with probability 0.75. A Patriot Party member might switch to Freedom Party with probability 0.05, become an independent with probability 0.10, or remain in Patriot Party with probability 0.85. An independent might join Freedom Party with probability 0.25, oin Patriot Party with probability 0.10, or remain independent with probability 0.65. Construct the transition probability matrix. a) b) Given that Alex was a Freedom Party member in 2017 and is an independent in 2018, what is the probability that he will be a Patriot Party member in 2019? c) Given that Alex was a Freedom Party member in 2017, what is the probability that he is an independent in 2018 and will be a Patriot Party member in 2019?Explanation / Answer
Probability F P I
F 0.75 0.10 015
P 0.05 0.85 0.10
I 0.25 .10 0.65
b) P( P in 2019 given that I in 2018) = 0.10 from the tables
c) P( Independet in 2018 and Patrio in 2019 / FP in 2017) = 0.15 * 0.10 = 0.0150
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