11. The results above are based on Central Limit Theorem . 12. The central limit theorem implies that those statistical parameters will have asymptotically normal distributions. 13. If in addition each has finite variance, then by the central limit theorem , 14. To apply the central limit theorem , one must use a large enough sample. 15. The thermodynamic limit is essentially a consequence of the central limit theorem of statistics. 16. By the way, pairwise independence cannot replace independence in the classical central limit theorem . 17. This confidence can actually be quantified by the central limit theorem and other mathematical results. 18. For the purposes of normally distributed, an assumption justified by the Central Limit Theorem . 19. He made important contributions to central limit theorems and the theory of alpha stable distributions. 20. Similarly, Brouwer's theorem is used for the proof of the Central Limit Theorem .