Download PDF by Fazlollah M. Reza: An Introduction to Information Theory

By Fazlollah M. Reza

Info thought

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A (B + AC. + C) = FIG. 2-9. Distributive law. ---..... /' " A '\. "- 2-10. FIG. --. ,, ~~~ (A /' - ....... / r \ '\. ,A "- "'- + B)' = FIG. A'B'. A' ......... "" B'. A+B=B+A AB = BA Associaiioe Laws: +C = A + + C) (AB)C = A(BC) Distributive Laws: A(B A + + BC + C) = AB AC = (A B)(A C) + + Complementarity: A + A' == U 0 A+U=U AA' = AU = A A +0= A A0 = - 2-11. Dualisation. + Commutative Laws: + B) - 0 Difference Law: CAB) + (A - B) = A (AB)(A - B) = 0 A - B = AB' "'" + BC '\. """ Dualization. A + B) (A + C).

What is the probability of the card being either red or a king? Solution. Let A be the event that the card is red, and B the event that the card is a king. The event of interest is A + B. Where A and B are not exclusive events, apply Eq. (2-67): PIA} = }~ P{B} = }13 P{AB} = (}ls)(}~) = }~6 PIA B} = ~~ ~ls - ~~6 = Xs + + Example 2-14. An honest coin is tossed 10 times. What is the probability of having at least (a) one tail and (b) two tails? Solution. The main assumption in this and in similar problems is the concept of independence of successive trials and the equally probable outcomes.

A) Thevenin's partitioning. network. (b) Bayes's partitioning. FIG. At, a part of the network; A 2, the remainder sets containing a number of subevents. Electrical engineers may note that Bayes's rule is somewhat similar to 'I'hevenin's theorem in network theory. 'I'hevenin's theorem permits a partitioning of the network into two parts and a study of the system with respect to one pair of terminals of the partitioned boundary. Bayes's theorem, like Thevenin's theorem, can be extended to a partitioning of the sample space into mutually exclusive and exhaustive parts.

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