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 = [ 0.8 0.19999999999999996 ]
[ 0.30000000000000004 0.7 ]
and initial distribution v₀ = (0.4, 0.6). Find v₁ (to 2 decimal places).
Working
- 1v₁(state 1) = 0.4·0.8 + 0.6·0.30000000000000004 = 0.5.
- 2v₁(state 2) = 0.4·0.19999999999999996 + 0.6·0.7 = 0.5.