Given n events A 1, A 2, · ··, An , bounds are obtained for the probability of the occurrence of at least m out of the n events. The bounds are linear in terms of S 1 and S 2 where S 1 = Σi P(Ai ) and S2 = Σ i<j Ρ (Α i ,Α j ). The bounds are illustrated with an example. For m = 1 the bounds are the same as the best known linear bounds in terms of S 1 and S 2.

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Given n events A1, A2, · ··, An, bounds are obtained for the probability of the occurrence of at least m out of the n events. The bounds are linear in terms of S1 and S2 where S1 = Σi P(Ai) and S2 = Σi<jΡ (Α i,Α j). The bounds are illustrated with an example. For m = 1 the bounds are the same as the best known linear bounds in terms of S1 and S2.

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Sharp upper and lower bounds for the variance and the distribution of the Graybill-Deal estimator of ihe common mean μ of two independent normal distributions with unknown variances are obtained in case of equal sample sizes.