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Consider a treatment-control experiment with N units where for each unit 1' we observe a pre- treatment {i.e., not affected by treatment) oovariate Xi. Let if!\" he the observed eovariate mean for the treatment group and if?\" he the observed eovariate mean for the control group. Prove that under a oomplete randomization with $11 units assigned to treatment and nu units assigned to oontrol, these means are equal in expectation. That is? prove that E[X'f""] = E[X3i\"]