On the Sum of Symmetric Random Variables |
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| Authors: | Robert Chen Larry A Shepp |
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| Institution: | 1. Department of Mathematics , University of Miami , Coral Gables , FL , 33124 , USA;2. Department of Discrete Mathematics , Bell Laboratories , 600 Mountain Avenue, Murray Hill , NJ , 07974 , USA |
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| Abstract: | Let U and V be two symmetric (about zero) random variables with U + V symmetric about C; here C is a constant. It is easy to see that if U and V are mutually independent, or if both U and V satisfy the weak law of large numbers, then C = 0. So, intuitively, we would suspect that C = 0 in general. However, we show that there exist two random variables U and V symmetric about 0 with U + V symmetric about C ≠ 0 The example given is closely related to one given by Alejandro D. De Acosta in another context. |
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