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Note that $Y_1$ and $Y_2$ are identically distributed. We have $\text{cov}(Y_1,Y_2) = E[Y_1Y_2] - E[Y_1]E[Y_2] = E[X_1^2X_2^2/(\sum_i X_i^2)^2]-E[X_1^2/\sum_i X_i^2]^2$ Can you use this? Can Jensen's inequality be applied?



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