By Fazlollah M. Reza

ISBN-10: 0486682102

ISBN-13: 9780486682105

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**Sample text**

The intuitive concept of frequency requires a considerable amount of clarification before it becomes mathematically acceptable. This can be done in the light of the laws of large numbers. The section may be omitted by those who prefer mathematical accuracy to physical justification. BABIC CONCEPTS OF DISCRETE PROBABILITY honest person under nresenbed eireumstances. that o ~ n(X s k) N o < n(Xk ) < 1 - N -o < lim n(Xk ) < 1 - N--+oo N - Equation (2-49) states that the probability of any event X k is a real number in the real interval [0,1].

The four events are independent but not necessarily mutually exclusive. The event of interest is E = E IE 2 + E aE 4 PtE} =P{E IE 2 + E aE 4 } = P{E IE 2} + P{E aE4 } - P{E IE 2E aE 4 } PtE} = P{EdP{E 2 } + P{E3}P{E~} - P{EdP{E 2}P{E 3}P{E4 } PtE} = 20: 2 - 0: 4 46 DISCRETE SCHEMES WITHOUT MEMORY Note that o :::; PlO} = 0 P{l} = 1 P {E} S 1 for 0 :::; a S 1 In many we wish to concentrate on two mutually exclusive and exhaustive events of the sample space, that is, two events and A 2 such that A lA 2 Al +A 2 = (1 = (2-87) U The assumption is that each of these events has a subevent of special interest to us.

2-103) Every permutation of elements of a set contains the same elements but in different order. When two sets of objects are in one-to-one correspondence so that some of the elements of one do not appear in the other they are called different combinations. For example, if we combine the members of the set {A,B,C,D} two by two, AB, AC, DB are different binations but AB and BA are not. The number of different combinations of n objects taken r at a time is P» c» = rT = n! (n _ r)! (2-104) When confusion will not result, one may use the notation (;) for C/'.

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