The distribution of mean intensities of cDNA spots corresponding to genes that are expressed can be assumed to be normal [276]. Consider an array on which there are both expressed and unexpressed genes. Let us assume that the mean of the distribution corresponding to the expressed genes is 1,000 and the standard deviation is 100; the mean of the distribution corresponding to the unexpressed genes is 400 and the standard deviation is 150 (usually there is higher variability in the low intensity spots). We are using an array that has each gene spotted in triplicates. We calculate the expression value of a gene as the mean of its replicates.

(a) What is the probability that a spot corresponding to an expressed gene has a value lower than 700?

(b) What is the probability that an expressed gene has an expression value of 700 or lower?

(c) Find the threshold T in the intensity range corresponding to the intersection point of the two distributions (the point for which the probability of having an expressed gene is equal to the probability of having an unexpressed gene).

(d) What is the probability that an expressed gene has the mean of its replicates lower than T? (This would be a false negative.)

(e) What is the probability that an unexpressed gene has the mean of its replicates higher than T? (This would be a false positive.)

(f) What is the probability that an individual spot corresponding to an expressed gene has an intensity lower than T? (This would be a false negative on an array not using replicates.)

(g) What is the probability that an individual spot corresponding to an unexpressed gene has an intensity higher than T? (This would be a false positive on an array not using replicates.)