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Type 19 Auto Content Shortcuts - ' 151% ? 16 The logical basis for the definition of statistical independence is best seen in terms of conditional probabilities and is most appealing from a subjective view of probability, Suppose that I believe the probability that event A will occur is P(A). Then I am given the information that event B has occurred. If this new information does not change my view of the probability of A, then P(A) = P(AB), and the information about the occur rence of B is of no value in determining P(A). This definition of statistical independence agrees with a commonsense notion of independence. To help understand independence, we present a revised version of our photo and messaging problem in Table 3.5. In this case the marginal probabilities of messaging and photo capabilities are the same, but their us- age is independent. Note how the preceding definitions for independence yield a conclu- sion of independence for Table 3.5 but not for Table 3.4 MESSAGING NO MESSAGING Photo 0.60 (1.20 (180 ant Probability Photo and ssaging When ey Are dependent No photo 0.15 (105 0.20 11.75 025 10 In our following discussions we refer to events being independent. For example, the events "Dos Jones will rise and neckties are wider are independent Whatever I be lieve about the likelihood of the latter will not intluence my judgment of the chances of the former lumple 3 18 illustrates a test for independence Zoom: Q Address Links Desktop Local Disk (D:) @ $40