caa a22 4500 386350450 CHVBK 20180307111827.0 cr unu---uuuuu 161130e198910 xx s 000 0 eng 10.1017/S0269964800001339 doi S0269964800001339 pii (NATIONALLICENCE)cambridge-10.1017/S0269964800001339 The Central Limit Theorem and the Law of Large Numbers for Pair-Connectivity in Bernoulli Trees [Elektronische Daten] Consider the standard network reliability model in which each edge of a given (n, m)-graph G is deleted, independently of all others, with probability q = 1- p (0 <p < 1). The pair-connectivity random variable X is defined to be the number of connected pairs of vertices that remain in G. The mean of X has been proposed as a measure of reliability for failure-prone communications networks in which the edge deletions correspond to failures of the communications links. We consider deviations from the mean, the law of large numbers, and the central limit theorem for X as n → ∞. Some explicit results are obtained when G is a tree using martingale difference sequences. Stars and paths are treated in detail. Copyright © Cambridge University Press 1989 Siegrist Kyle T. Department of Mathematical Sciences The University of Alabama in Huntsville Huntsville, Alabama 35899 Amin Ashok T. Department of Computer Science The University of Alabama in Huntsville Huntsville, Alabama 35899 Slater Peter J. Department of Mathematical Sciences The University of Alabama in Huntsville Huntsville, Alabama 35899 Probability in the Engineering and Informational Sciences Cambridge University Press 3/4(1989-10), 477-491 0269-9648 3:4<477 1989 3 PES https://doi.org/10.1017/S0269964800001339 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0269964800001339 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Siegrist Kyle T. Department of Mathematical Sciences The University of Alabama in Huntsville Huntsville, Alabama 35899 NATIONALLICENCE 700 1- Amin Ashok T. Department of Computer Science The University of Alabama in Huntsville Huntsville, Alabama 35899 NATIONALLICENCE 700 1- Slater Peter J. Department of Mathematical Sciences The University of Alabama in Huntsville Huntsville, Alabama 35899 NATIONALLICENCE 773 0- Probability in the Engineering and Informational Sciences Cambridge University Press 3/4(1989-10), 477-491 0269-9648 3:4<477 1989 3 PES CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge