Statistical Analysis of Hairpins and BasePairs in RNA Secondary Structures
AJ Bu, Manuel Kauers, Doron Zeilberger
TL;DR
Convincing evidence is given that the central-scaled distribution of the pair of random variables (hairpins, basepairs) tends in distribution to the bi-variate normal distribution with correlation.
Abstract
We derive precise asymptotic expressions for the expectations, variances, covariance, and quite a few further mixed moments for the number of hairpins and the number of basepairs in RNA secondary structures, and give convincing evidence that the central-scaled distribution of the pair of random variables (hairpins, basepairs) tends in distribution to the bi-variate normal distribution with correlation $\sqrt{5 \sqrt{5} -11}/2= 0.2123322205\dots$