Math Problem Solver

Consider a simple marriage model represented as a Markov process with three states:

single

married

divorce

The transitional probabilities between these states are as follows:

P_{11} &= 0.3, P_{12} = 0.21, P_{13} = 0.49 (from Single)

P_{21} &= 0.2, P_{22} = 0.64, P_{23} = 0.16 (from Married)

P_{31} &= 0.2, P_{32} = 0.24, P_{33} = 0.56 (from Divorced)

starting with a population where 46% are Single, 22% are Married, and 19% are Divorced.

Calculate the probabilities of being in Single after one time period

Answer for part 1

Calculate the probabilities of being in Married after one time period

Answer for part 2

Calculate the probabilities of being in Divorced after one time period

Answer for part 3