Geodesic
A Note on Bernstein's Bivariate Inequality
Canadian mathematical bulletin, Tome 22 (1979) no. 3, pp. 371-375

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An upper bound for P[Σ Xi≥tσ, Σ Yi ≥ tσ], where (Xi, Yi ), i = 1, 2, ..., n are bounded independent random variables, was given by Mullen (1973). An improvement to the bound is possible without further assumptions. 
Mullen, K. A Note on Bernstein's Bivariate Inequality. Canadian mathematical bulletin, Tome 22 (1979) no. 3, pp. 371-375. doi: 10.4153/CMB-1979-048-4
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     title = {A {Note} on {Bernstein's} {Bivariate} {Inequality}},
     journal = {Canadian mathematical bulletin},
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     year = {1979},
     volume = {22},
     number = {3},
     doi = {10.4153/CMB-1979-048-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1979-048-4/}
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