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Dec 14, 2012 at 22:31 comment added whuber This is incorrect because you are following a different convention for subscripting the $X$'s: they start at $0$, not $1$. Bear in mind, too, that the convention with Markov chains is to right multiply by the transition matrix. You can always tell which convention is in use by checking the sum-to-unity condition. By multiplying on the left by this $P$, whose rows sum to unity, you are not computing correctly.
Dec 14, 2012 at 19:19 history answered Mimshot CC BY-SA 3.0