One step of a Markov chain
Guided practice — solve each problem, check, then generate a fresh one.
Formula to apply
v₁ = v₀ · P
Problem
A 2-state Markov chain has transition matrix
P = [ 0.6 0.4 ]
[ 0.30000000000000004 0.7 ]
and initial distribution v₀ = (0.6, 0.4). Find v₁ (to 2 decimal places).
Working
- 1v₁(state 1) = 0.6·0.6 + 0.4·0.30000000000000004 = 0.48.
- 2v₁(state 2) = 0.6·0.4 + 0.4·0.7 = 0.52.