Summary: We give a pair of well-matched lower and upper bounds for the expectation of reversal distance under the hypothesis of random gene order by investigating the expected number of cycles in the breakpoint graph of linear signed permutations. {\it D. Sankoff} and {\it L. Haque} [The distribution of genomic distance between random genomes, J. Comput. Biol. 13, 1005‒1012 (2006)] proved similar results for circular signed permutations based on approximations based on a slightly different model; while our approach is discrete. We also provide a near-tight upper bound for the variance of reversal distance, which gives information on the distribution of reversal distance.