Suppose that we have a fair dice, the theoretical frequency of an event 'the dice shows a three' is 1/6, (if the dice is assumed fair, the theoretical frequency is the same for any number from 1 to 6). In that case a hypothetical experimentalist guessing will have an average expected surprise of H[X] = log 2 (6) . We note the two natural bounds that the entropy can have. The Shannon Entropy of an ensemble X is always greater or equal to zero. It can only be zero if p(x~a i )~1 for only one of the N elements of A X~f a 1 ,a 2 ,:::,a i ,:::,a N g. On the other hand, the Shannon Entropy is maximized in the case that p(x~a i )~1=N. This is the so-called ''equiprobable distribution'', a uniform probability distribution over the finite set. Transcriptional Shannon Entropy. Let f (j) i the expression value of probe i (i = 1,…, N) on sample j (j = 1, …, M). For each sample j we first normalize the expression values. We interpret them as the theoretical frequency of a single hybridization event. We then define a probability distribution function (PDF) over a finite set as: The uniform (equiprobably) distribution is defined as i Let H e~H ½P e ~log 2 N, then in this paper we always use the Normalized Shannon Entropy, defined as: