IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Markov chains
In a Markov chain with transition matrix P, which condition must every row of P satisfy?
Every row of a transition matrix must have non-negative entries that sum to one, because each row is the probability distribution of the next state given the current state. Entries may be zero, and no other restriction applies.
- AEntries sum to one and each is non-negativeCorrect
- BEntries sum to zero
- CEntries are all equal
- DDiagonal entry is the largest
- Entries are strictly positive
Explanation
Each row is a probability distribution over next states, so entries are non-negative and sum to one. Zeros are allowed, diagonals need not be largest.
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