2. Let X0, X1,... be an irreducible DTMC with transition matrix P and invariant measure y...

Transcribed Image Text:

2. Let X0, X1,... be an irreducible DTMC with transition matrix P and invariant measure y where y is strictly positive. (a) Is Q a stochastic matrix where Q(i, j) = y(j)P(j, i) y(i) (b) Prove or disprove: Pi{X = j1,, Xn = jn} = Y(jn) y(i) -Q(n, n1)Q(jn1, n2) Q(j1, i). 2. Let X0, X1,... be an irreducible DTMC with transition matrix P and invariant measure y where y is strictly positive. (a) Is Q a stochastic matrix where Q(i, j) = y(j)P(j, i) y(i) (b) Prove or disprove: Pi{X = j1,, Xn = jn} = Y(jn) y(i) -Q(n, n1)Q(jn1, n2) Q(j1, i).