IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov processes
A two-state chain (states A and B) has P(A→B) = 0.2 and P(B→A) = 0.4. What is the long-run stationary probability of being in state A?
Set the flow from A to B equal to the flow from B to A: 0.2πA = 0.4πB, so πA = 2πB. With probabilities summing to one, the stationary probability of A is 2/3.
- A1/3
- B0.4
- C0.5
- D2/3Correct
- 0.8
Explanation
Balance: πA×0.2 = πB×0.4, so πA = 2πB. With πA + πB = 1, πA = 2/3. Choosing 1/3 swaps the two flow rates.
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