ales report from a public company, namely: XEX= {good, same, bad} = {x1,x2,x3}, meaning that the results are in excess of the predictions (good), or on target (same), or under target (bad). The second event source is the company's stock value, as reflected by the stock exchange, with ye) = {up, steady, down} = {y1, y2, y3}. Then we assume that there exists some form of correlation between the company's results (x E X) and its stock value (yey). A numerical example of joint and con- ditional probability data, p(xi,yj), p(xilyj) and p(yj|xi), is shown in Table 5.1. The first group of numerical data, shown at the top of Table 5.1 corresponds to the joint probabilities p(yj, Xi) Summing up the data by rows (i) or by columns (j) yields the probabilities p(xi) or p(yj), respectively. The double checksum (bottom right), which yields unity through summing by row or by column, is also shown for consistency. The two other groups of numerical data in Table 5.1 correspond to the conditional probabilities p(xilyj) and p(yj|xi). These are calculated through Bayes's theorem p(xilyj) = p(xi,yj)/p(yj) and p(yj|xi) = p(xi,yj)/p(xi). The intermediate columns providing the data p(xilyj)p(yj) = p(yj|xi)p(x) = p(xi,yj) and their check- sums by column are shown in the table for consistency. 2 Yet we have the property = 1 for any event b E B, summing over all possible events a E A. Mutual information and more entropies Table 5.1 Example of joint and conditional probability distributions constructed from the two event sources X E X = {good, same, bad} = {X1, X2, X3} for a company's quarterly sales results and y E Y : {up, steady, down} = {y1, y2, y3} for its stock value. The table on top shows the joint probability p(x,,jj), consistent with the probabilities p(xi) and 1(p(yj) of the individual events Xi and yj (values given in column or line p, respectively). The right column and bottom line provide the different checksums. The two other tables (middle and bottom) show the conditional probabilities p(y) |Xi) and p(xilyj), along with thei