This preview shows page 1. Sign up to view the full content.
Unformatted text preview: uity analysis. For example, we can transform the hypothetical census in Fig.2(ii)a into a binary map (Fig.2(iv)b) by defining empty cells as white, and cells containing at least one point as black. The simplest form of contiguity analysis is concerned with tests based on the sampling theory of the distribution of contacts between cells. These contacts are defined as white-white, black-white 8 given in equation (7). Two events are said to be independent if the occurrence of one event in an experiment does not influence the occurrence of the other. The idea of independence is defined in the multiplication axiom which states that, if E 1 9 product of their individual probabilities'. Symbolically we write this definition as (12) (15) Conversely, the probability that the point does not land in the specified cell, such that the complementary event occurs, is given by (16)
For example, in our unbiased coin tossing experiment the multiplication axiom gives the probability of Heads being followed by tails in two tosses of the coin as More generally, for experiments with n outcomes, the multiplication axiom may be written as (13) we take a single one of these sequences we can use the multiplication axiom to obtain the probability of its occurrence. The event E occurs m times in the sequence, each time w...
View Full Document