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In the development of a new receiver for the transmission of digital information, each received bit is rated as acceptable, suspect, or unacceptable, depending on the quality of the received signal, with probabilities 0.9, 0.08, and 0.02, respectively. Assume that the ratings of each bit are independent. In the rst four bits transmitted, let X denote the number of acceptable bits Y denote the number of suspect bits Then, the distribution of X is binomial with n 4 and p 0.9, and the distribution of Y is binomial with n 4 and p 0.08. However, because only four bits are being rated, the possible values of X and Y are restricted to the points shown in the graph in Fig. 5-1. Although the possible values of X are 0, 1, 2, 3, or 4, if y 3, x 0 or 1. By specifying the probability of each of the points in Fig. 5-1, we specify the joint probability distribution of X and Y. Similarly to an individual random variable, we de ne the range of the random variables (X, Y ) to be the set of points (x, y) in two-dimensional space for which the probability that X x and Y y is positive.

4.10 10 5 f X Y (x, y)

354 10

NOTE: Data for the W-B I and WAIS are from Wechsler (1958, Tables 9 and 10). Data for the WAIS-R are based on sample sizes for the total standardization group provided in Table 1 by Reynolds et al. (1987). Data for the WAIS-III are from the WAIS-III/WMS-III Technical Manual (Psychologi-

5 1.84 10 3 3 4.10 10

cal Corporation, 1997, Table 2.6). The group listed as 8 or less for the W-B I is actually a combination of percentages provided for elementary school graduates, those with some elementary school, and illiterates.

1.54 10 5 1.38 10 3 3.11 10 2

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[Gol99] and [Sil03]. These are data structures associated with a file in which each entry defines a subject that can access the file and its permitted access modes. The pattern models the entries of the ACLs but not the fact that they are associated with the file components.

Figure 5-1 Joint probability distribution of X and Y in Example 5-1.

the time (which would have made it understandable to omit non-Caucasians from the W-B I sample), it is reasonable to conclude that the standardization samples of the four adult Wechsler batteries are appropriately comparable.

6 3.46 10 4 1.56 10 2 0.2333 1 2.56 10

bina, 1997) will be examined for the W-B I, WAIS, WAIS-R, and WAIS-III: internal consistency (correlations between each subtest and total score on the battery), factor analysis, and developmental changes (progression of mean Verbal, Performance, and Full Scale scores across the age range).

Other aspects of using this pattern include:

1.6 10 7

Construct validity, which determines the degree to which a test measures the traits or constructs it was developed to measure, is considered by Messick (1980) to be the only real type of validity. More than a comparison of reliability coefficients, content changes, or standardization samples, a comparison of the constructs underlying the three adult Wechsler test batteries is instrumental in deciding whether the bulk of research obtained on the W-B I, WAIS, and WAIS-R is legitimately generalizable to the WAIS-III. Three of the types of acceptable evidence in support of a test s construct validity (Anastasi & Ur-

2.88 10 5 1.94 10 3 5.83 10 2 0.6561

If X and Y are discrete random variables, the joint probability distribution of X and Y is a description of the set of points (x, y) in the range of (X, Y ) along with the probability of each point. The joint probability distribution of two random variables is sometimes referred to as the bivariate probability distribution or bivariate distribution of the random variables. One way to describe the joint probability distribution of two discrete random variables is through a joint probability mass function. Also, P(X x and Y y) is usually written as P(X x, Y y). De nition The joint probability mass function of the discrete random variables X and Y, denoted as fXY (x, y), satis es (1) (2) (3) fXY 1x, y2

Some systems use the concept of Owner, who has all rights on the files they create. The Owner in this model corresponds to a special type of subject. When roles are used, there are no owners and when groups are used, ownership is not inherited in subgroups. In some systems, files are mapped to the virtual memory address space. The pattern still applies to this case, although a more uniform solution is then possible (see CONTROLLED VIRTUAL ADDRESS SPACE (339)). In some systems, the directory is not strictly a tree, because it is possible to have links between files in different subtrees [Sil03]. Modeling this case would require adding some associations to the model shown in the figure AUTHENTICATOR (324).

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