Let qm = P(X ≤ m), where m is a positive integer and X a binomial random variable with parameters n and m/n. Vašek Chvátal conjectured that, for fixed n ≥ 2, qm attains its minimum when m is the integer closest to 2n/3. As shown by Svante Janson, this conjecture is true for large n. Here, we prove that the conjecture is actually true for every n ≥ 2. © 2022 Elsevier B.V. All rights reserved.
Barabesi, L., Pratelli, L., Rigo, P. (2023). On the Chvátal–Janson conjecture. STATISTICS & PROBABILITY LETTERS, 194, 1-6 [10.1016/j.spl.2022.109744].
On the Chvátal–Janson conjecture
Barabesi L.;
2023-01-01
Abstract
Let qm = P(X ≤ m), where m is a positive integer and X a binomial random variable with parameters n and m/n. Vašek Chvátal conjectured that, for fixed n ≥ 2, qm attains its minimum when m is the integer closest to 2n/3. As shown by Svante Janson, this conjecture is true for large n. Here, we prove that the conjecture is actually true for every n ≥ 2. © 2022 Elsevier B.V. All rights reserved.
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https://hdl.handle.net/11365/1224894