Let 0 , 1 , be a sequence of nonnegative numbers such that Consider a Markov chain X 0 , X 1

Let α₀, α₁, ⋯ be a sequence of nonnegative numbers such that

Consider a Markov chain X₀, X₁, X₂, ⋯ with the state space S = {0, 1, 2,⋯} such that

Show that X₁, X₂, ⋯ is a sequence of i.i.d random variables.

; = 1. j=0