Brownian Moton in the Stock Market l51 for both intervals the distributions are nearly normal in ratio unIts ThIs Is slightly less true for percentage unIts in which the data was orginally published The effect Is less noticeable in the monthly data, where the percentage changes are small, and hence nearly equivalent to ratio unIts his nearly normal distribution in the changes of logarithm of prices uggests that It may be a consequence of many independent random vanables contributing to the changes in values(as defined by the Weber Fechner The normal dIstribution arses In many stochastIc proc o0o d03 Fig 7 Cumulated distrbutions of Aloge P=logeIP(+r)/P(e] for 1=1 (NYSE common stocks) These, and also Fig distrIbutions of S()for fixed M*() sold line is the distrbution of Z)M(), transcrIbed from Fig 12 for comparison esses involving large numbers of ndependent variables, and certaInly the market place should fulfill this condition, at least 4. As a fourth element in our analy sIs, we would lke to define alog Ision As an elementary example let us suppose we must make a decision urse of action A, and course of action b We know, or can estimate ense)that course of action A has possible outcomes Yal, yt with probabilties p(Yan),(Ya2), ete, whIle a decision for b has possble outcomes YBl, YB2, wIth probabIlties p(YB,P(Y 2), ete Then the logieal choice 1s to make a decision for A, or B, for whuch the expectation value, & of the outcome, &(YA)-E, YA, P(Yad) or 8(rB)=X,YB, (YB, is the larger