What the markov property does not mean

Reference no: EM13966518

1. Suppose fXng is a stationary Markov chain. Prove that for all n and all xi ;i D 0; 1; :::;n C 2; P.XnC2 D xnC2; XnC1 D xnC1 jXn D xn ; Xn-1 D xn-1;::: ; X0 D x0/ D P.XnC2 D xnC2; XnC1 D xnC1 jXn D xn/.

2. ( What the Markov Property Does Not Mean). Give an example of a stationary Markov chain with a small number of states such that P.XnC1 D xnC1 jXn xn; Xn-1 xn-1;::: ; X0 x0/ D P.XnC1 D xnC1 jXn xn /is not true for arbitrary x0; x1;::: ; xnC1.

3. (Ehrenfest Urn). Consider the Ehrenfest urn model when there are only two balls to distribute.

(a) Write the transition probability matrix P.

(b) Calculate P 2;P 3.

Reference no: EM13966518

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