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higher-level languages, 2 3 Hollerith, Herman, 8 Hopper, Grace Murray, 10 HTML (hypertext markup language), 135 137 HTTP (hypertext transport protocol), 134 135 IBM (International Business Machines Corporation), 8 imperative language, 46, 49 inheritance, 52, 78, 79, 81 82 insertion sort, 17 19 instance method, 51, 52, 78, 79 80 instance variable, 51, 52, 78, 79 80 instruction set. See machine language International Business Machines Corporation (IBM), 8 internet, 128 reference model, 129, 129 134 internet protocol (IP), 131 132 interpreter, 48 49 I/O, 40-1 direct memory access (DMA), 100 interrupt-driven, 100 management, 99 memory mapped, 101 programmed, 100 See also Java: input/output IP (internet protocol), 131 132, 133 134 ISO OSI reference model, 128, 128 129 iteration. See looping Jacquard, Joseph Marie, 5 Jacquard loom, 5, 7 Java, 47, 49, 50 51, 66 control structures, 71 77 data types, 66 70 error handling, 85 87 identifiers, 71 input/output, 87 92 interfaces, 83 84 operators, 70 variables and methods, 79 84 Java Virtual Machine (JVM), 49 JDBC, 162 165 job control language (JCL), 97 LAN (local area network), 127 128. See also network languages design properties of, 59 60 history of, 44 47, 59 syntax and semantics of, 61 64 See also compiler; interpreter; specific language

Table 7-3 shows the values of b corresponding to given values of p as obtained in Problems 7.23 and 7.24. Note that b represents the probability of accepting the hypothesis p 0.5 when actually p is a value other than 0.5. However, if it is actually true that p 0.5, we can interpret b as the probability of accepting p 0.5 when it should be accepted. This probability equals 1 0.0358 0.9642 and has been entered into Table 7-3.

1 2 3 4 5 6

Table 7-3 p b 0.1 0.0000 0.2 0.0000 0.3 0.0192 0.4 0.5405 0.5 0.9642 0.6 0.5405 0.7 0.0192 0.8 0.0000 0.9 0.0000

The Show command is useful for plotting several graphs simultaneously, particularly when their domains are different intervals.

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(a) The graph of b vs. p, shown in Fig. 7-7(a), is called the operating characteristic curve, or OC curve, of the decision rule or test of hypotheses. The distance from the maximum point of the OC curve to the line b 1 is equal to a 0.0358, the level of significance of the test. In general, the sharper the peak of the OC curve the better is the decision rule for rejecting hypotheses that are not valid. (b) The graph of (1 b) vs. p, shown in Fig. 7-7(b), is called the power curve of the decision rule or test of hypotheses. This curve is obtained simply by inverting the OC curve, so that actually both graphs are equivalent. The quantity 1 b is often called a power function since it indicates the ability or power of a test to reject hypotheses which are false, i.e., should be rejected. The quantity b is also called the operating characteristic function of a test.

5 18 42 27 8 100

EXAMPLE 4 Suppose we wish to plot the graph of y = x2 9 on the interval [ 4, 4] and the graph of y = sin x on the interval [0, 2 ], but wish to plot them on one set of axes. We define two graphics objects, g1 and g2.

Fig. 5-1

lexical analysis, 61 64 LISP, 46, 55 57 local area network (LAN), 127 128. See also network looping, 57 58, 72 74 Lovelace, Augusta Ada, 7 machine instruction set. See machine language machine language, 2, 36 39, 44 45, 95 96 Mark I, 9 10 Mauchly, John, 11 memory, 39 40 management, 116 122 merge sort, 19 22 methods instance, 51, 52, 78, 79 80 static, 52 53, 79 80 monitors, 108 109 multiprogramming, 97 network, 3, 127 protocol, 127 134 wireless, 131 normalization, 145 147 NSFnet, 134 object, 78. See also object-oriented programming object code, 48 object-oriented language, 46 47, 66 67 object-oriented programming, 51 53, 77 82 Open Systems Interconnection (OSI) model, 128, 128 129 operating systems, 3, 96 97 embedded system, 99 file systems and, 122 124 history of, 97 98 memory management and, 116 122 multiprocessor, 98 99 process scheduling and, 101 116 real-time, 99 order of growth (Q), 17 Q(lg n), 23, 24 Q(n), 17, 24 Q(n!), 24, 24 25 Q(n2), 18 19, 24 Q(n lg n), 21 22, 24 Q(2n), 23 24, 24 paging, 118 122 parse tree, 62 64 parsing. See syntax analysis

g1 = Plot[x2 9, {x, 4, 4}]

interest that the shape of the graph seems to indicate that the sample is drawn from a population of heights that is normally distributed.

If in Table 5-2 we recorded the relative frequency or percentage rather than the number of students in each class, the result would be a relative, or percentage, frequency distribution. For example, the relative or percentage frequency corresponding to the class 63 65 is 18>100, or 18%. The corresponding histogram is then similar to that in Fig. 5-1 except that the vertical axis is relative frequency instead of frequency. The sum of the rectangular areas is then 1, or 100%. We can consider a relative frequency distribution as a probability distribution in which probabilities are replaced by relative frequencies. Since relative frequencies can be thought of as empirical probabilities (see page 5), relative frequency distributions are known as empirical probability distributions.

g2 = Plot[Sin[x], {x, 0, 2 o}]

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