Differences in random variables and estimating second moments

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Suppose $S=\{{X_1,X_2,...,X_n}\} $ is a set of random variables with finite moments. If we know the first moment of all of these variables, and also we have many observations on $\{{X_1-X_2,X_1-X_3,X_1-X_4,...,X_1-X_n}\} $ do we have anything to say in general about the second moment of $X_1$ given these observations?