By Luisa Vergani

ISBN-10: 0822003910

ISBN-13: 9780822003915

Cliffs Notes on Divine Comedy: Inferno

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**Additional resources for Dante's Divine Comedy: The Inferno (Cliffs Notes)**

**Example text**

9 where n parallel levels are depicted and each level j contains a series of rj phases connected, each with exponentially distributed time and rate r j p j . Each level j is selected with probability j . The pdf is given by Another type of generalized Erlang distribution can be obtained by lifting the restriction that all the phases within the same level have the same rate, or, alternatively, if there are nonzero exit probabilities assigned such that remaining phases can be skipped. These generalizations lead to very complicated equations that are not further described here.

83) where P ( T > t n - l i a / 2 ) = a/2. If a maximum likelihood estimation is used for the point estimation it is convenient to use likelihood ratio confidence bounds as they can directly reuse the result of the point estimation. These are defined as [MeEs98] L(8) >e-;. 84) L(8) - that was found by the point estimation, xi,, is the X2-quantile with k degrees of freedom, which is just the number of estimated parameters, and the error-probability a. An easy interpretation of Eq. 85) / by taking the natural logarithm ( g ( 8 ) is referred to as confidence function in the remainder of this section).

1 %-Transform Let X be a discrete random variable with the probability mass function pk = P ( X = k ) for k = 0 , 1 , 2 , .. , then thc z-transform of X is defined by The function G,(z) is also called the probability generating function. 4 specifies the probability generating functions of some important discrete random variables. 62) with k 3 a k ~= (-1) ( k - I ) ! , k(k - 1) ak,k-l = 2 ’ ~ k = 3 , 4 , . , k = 3 , 4 , .. , k - 2 . ) Parameter n ,P Binomial -P) +P4" Geometric P P. 2 Laplace Transform The Laplace transform plays a similar role for non-negative continuous random variables as the z-transform does for discrete random variables.

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