A Characterization of the Normal Distribution by the Independence of a Pair of Random Vectors

Wiktor Ejsmont

Kagan and Shalaevski 1967 have shown that if the random variables $X_1,\dots ,X_n$ are independent and identically distributed and the distribution of ${\sum }_{i=1}^n(X_i+a_i{)}^2$ $a_i…