# Markov property

I disagree with removing X_0 = i from the expectation in the first step of the following:

& = \sum_{j \in I} P(X_1 = j | X_0 = i) E(H^A | X_0 = i, X_1 = j) \\
& = \sum_{j \in I} p_{ij} E(H^A | X_1 = j) \quad \textrm{(by the Markov property)}\\
& = \sum_{j \in I} p_{ij} (1 + k_j^A)\\

It throws away the information that X_0 \notin A, which is relevant for the next rewrite step. The expected value of H^A clearly depends on what we know about X_0 and X_1.

Parting words from the person who closed the correction:
I disagree with removing X_0 = i from the expectation in the first step of the following: & = \sum_{j \in I} P(X_1 = j | X_0 = i) E(H^A | X_0 = i, X_1 = j) \\ & = \sum_{j \in I} p_{ij} E(H^A | X_1 = j) \quad \textrm{(by the Markov property)}\\ & = \sum_{
Status: Rejected
Reference to the user who closed the correction.:
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Status of the article (was it accepted?):
0
Status of the article (is it closed?):
1
What kind of correction is this:
Error