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In Sutton & Barto (2nd edition), the following is mentioned on page 150 (p. 172 of the pdf), section 7.4:

the importance sampling ratio has expected value one (Section 5.9) and is uncorrelated with the estimate.

How can we prove the importance sampling ratio is uncorrelated with the estimate?

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Sutton and Barto explain it themselves in section 5.9. I post it with a bit of context. The equation you're looking for is 5.13.Excerpt from Section 5.9

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