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How was the state transition probability matrix obtained for this example question? I hope you can provide help, thank you!
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Your link isn't working. – user469053 Mar 29 '24 at 01:07
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The $(i, j)$ entry of the transition matrix is the probability of going from state $i$ to $j$. Look in the $i$th row of the table, and see what number of claims will lead to state $j$. For example, if $(i, j)=(2,3)$ you see from the second row of the table that the only way to reach state 3 from state 2 is by having "1 claim" which has probability $a_1$, and this is the $(2,3)$ entry of the transition matrix. – angryavian Mar 29 '24 at 01:14