{"paper":{"title":"On some conjectures of Samuels and Feige","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Roland Paulin","submitted_at":"2017-03-15T13:45:16Z","abstract_excerpt":"Let $\\mu_1 \\ge \\dotsc \\ge \\mu_n > 0$ and $\\mu_1 + \\dotsm + \\mu_n = 1$. Let $X_1, \\dotsc, X_n$ be independent non-negative random variables with $EX_1 = \\dotsc = EX_n = 1$, and let $Z = \\sum_{i=1}^n \\mu_i X_i$. Let $M = \\max_{1 \\le i \\le n} \\mu_i = \\mu_1$, and let $\\delta > 0$ and $T = 1 + \\delta$. Both Samuels and Feige formulated conjectures bounding the probability $P(Z < T)$ from above. We prove that Samuels' conjecture implies a conjecture of Feige."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05152","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}