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In Section 7.1.2 Shannon information gain was interpreted as a measure of the difference between the joint probability distribution (represented by pij ) and the distribution that can be computed from the marginal distributions under the assumption that C and A are independent (represented by p.i p.j ). Clearly, if C and A are actually independent, this measure is zero. It can be shown (see below) that this is indeed the only case in which it is zero. For all other joint distributions this measure is greater than zero and it is the larger, the more strongly dependent the two attributes are. A different interpretation of this measure, which is preferred in connection to decision tree induction [Quinlan 1993], is based on the notion of the Shannon entropy of a set of alternatives [Shannon 1948]. Definition 7.2.1 Let S = {s1 , . . . , sn } be a finite set of alternatives having n positive probabilities P(si ), i = 1, . . . , n, satisfying i=1 P(si ) = 1. Then

state A as represented by the 3 1 transition. Eventually, the item is permanently xed and returned to the assembly line as represented by state 5. The lower half of the owgraph represents an analogous process for the less severe type B problems. This owgraph has two paths: 0 1 3 5 and 0 2 4 5. There are two rst-order loops and they do not touch each other. There is one secondorder loop, made up of the two nontouching rst-order loops. Table 2.2 gives a summary of the paths and loops along with their transmittances. For this owgraph, the MGF of the overall waiting time distribution i.e., the waiting time from 0 5, is found using (2.26): M(s) = where P1 (s) = p01 p35 M01 (s)M13 (s)M35 (s) P2 (s) = p02 p45 M02 (s)M24 (s)M45 (s) L1 (s) = p31 M13 (s)M31 (s) + p42 M24 (s)M42 (s) L2 (s) = p31 p42 M13 (s)M31 (s)M24 (s)M42 (s) L1 (s) = p42 M24 (s)M42 (s) 1 L2 (s) = p31 M13 (s)M31 (s). 1 P1 (s)[1 L1 (s)] + P2 (s)[1 L2 (s)] 1 1 , 1 L1 (s) + L2 (s) (2.28)

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Next, there developed a oor movement ostensibly aimed at preventing cannibalization of the successful pit-traded contract by its electronic upstart cousin If too much of the S&P trade was directed to the electronic screen, the argument went, it would jeopardize the liquidity of the successful pit contract To prevent such cannibalization, it was proposed that we place an upper limit on the quantity of any order that could be directed to the electronic venue Today such a thought would be laughable if not inane But in 1997, when electronic trade was still viewed in some quarters as the end of civilization, the idea was considered rational For me and our inner group, it was just one more obstacle in the long journey to electronic trade Any limitation of order size to Globex would act as an impediment to its success the lower this threshold, the higher the obstruction.

encryption. So that a subscriber cannot be followed around, it is frequently given a new TMSI (if the same TMSI were used for a while, a subscriber previously identi ed by some out of band means could be recognised by the TMSI). Theoretically, the IMSI should only have to be used on a subscriber s rst ever registration with any network, and it should be possible for the TMSI to be used even across different networks. In practice, however, the IMSI must be revealed on rst registration in a new network at least, and in some networks, more frequently than this. The GSM identity con dentiality is simple and ef cient, but is not robust. The IMSI must be revealed on rst registration with a network, and the mechanism as a whole can be compromised using a false base station as described later in this chapter.

# passwd -l carl Lock the user account (carl) Locking password for user carl. passwd: Success # passwd -u carl Unlock a locked user account (carl) Unlocking password for user carl. passwd: Success

1 The individual s wishes will harm me or others unnecessarily 2 The individual is reasoning erroneously he may be thinking illogically he may be deriving false conclusions, or he may have false beliefs (but, if so, then an attempt must be made to move him as soon as possible to the point where the autonomy ip can occur) Note: At this point in the Autonomy Test it is very important to bear in mind the distinction between physical autonomy the freedom that a person has to live without physical obstruction and mental autonomy the freedom that a person has to make decisions and act on them.

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