This could be a naive question but I am just puzzled. I am learning the following proof of Rao-Blackwell theorem but get puzzled by the equation in the red box. Why the two expectations can be reduced to one expectation? Thank you.
2026-04-04 05:19:39.1775279979
A question in the proof of Rao-Blackwell theorem
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This is an application of the law of total expectation.