Pattern discovery in DNA sequences is one of the most fundamental problems in molecular biology with important applications in finding regulatory signals and transcription factor binding sites. An important task in this problem is to search (or predict) known binding sites in a new DNA sequence. For this reason, all subsequences of the given DNA sequence are scored based on an scoring function and the prediction is done by selecting the best score. By assuming no dependency between binding site base positions, most of the available tools for known binding site prediction are designed. Recently Tomovic and Oakeley investigated the statistical basis for either a claim of dependence or independence, to determine whether such a claim is generally true, and they presented a scoring function for binding site prediction based on the dependency between binding site base positions. Our primary objective is to investigate the scoring functions which can be used in known binding site prediction based on the assumption of dependency or independency in binding site base positions.