A Note on Symmetric Random Variables

Burdick, David L.

Ann. Math. Statist., Tome 43 (1972) no. 6, p. 2039-2040 / Harvested from Project Euclid

Résumé

There exist independent random variables $X_1$ and $X_2$ such that $X_1$ is symmetric, $X_2$ is not symmetric, but $X_1 + X_2$ is symmetric. If $X_1$ and $X_2$ are i.i.d. random variables with a fractional moment and if for all real $\alpha P\lbrack X_1 + \alpha X_2 > 0\rbrack = \frac{1}{2}$ then they are symmetric.

Publié le : 1972-12-14
Classification:

@article{1177690880,
     author = {Burdick, David L.},
     title = {A Note on Symmetric Random Variables},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 2039-2040},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177690880}
}

Burdick, David L. A Note on Symmetric Random Variables. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  2039-2040. http://gdmltest.u-ga.fr/item/1177690880/