7.80. (Stationary Distribution.) If (π;) are stationary probabilities for (X+), then we have seen that \To = μπ₁, and for j ≥ 2, = (λj + μj)πj = λi−1πi−1 + µj+1πj+1. (7.41) Show that Tk = λολη-1 με... με • ΠΟ If C = 1 + x=1 λολη-1 με...μη < ∞, show that the stationary distribution is given by ñ = 1/C and (7.42) πn = 1 λο C με ...μη An-1 n ≥ 1. '
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