Abstract
In [Zaigraev, A., Kaniovski, S., 2010. Exact bounds on the probability of at least k successes in n exchangeable Bernoulli trials as a function of correlation coefficients. Statist. Probab. Lett. 80, 1079–1084] the authors present sharp bounds for the probability R k , n of having k successes out of n exchangeable Bernoulli trials, as a function of the marginal probability of success. The result is obtained by linear programming arguments. In this paper we develop further the result utilizing a geometrical approach to the problem, and find sharp bounds for R k , n given the marginal probability of success and the correlation among the exchangeable variables.
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