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1 | (18) |
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1 | (1) |
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1.2 Components of Rationality and Learning Model |
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2 | (2) |
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1.3 Predicate (Stochastic) Calculus for Psycho-Kinetics of Personality Development |
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4 | (6) |
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10 | (2) |
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12 | (1) |
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13 | (6) |
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17 | (2) |
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2 Decision Complexity and Methods to Meet Them |
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19 | (28) |
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2.1 Decision Complexities: Triangular Structure |
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19 | (2) |
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2.2 Vertex of Uncertainty (V1): Evidence of Probabilistic Thought During the Vedic and the Post-Vedic Period |
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21 | (2) |
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2.3 Probability and Its Measure as Discovered in European Continent |
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23 | (1) |
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2.4 Probability Distribution |
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24 | (1) |
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25 | (1) |
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2.6 The Vertex of Dependence (V2): Association and Their Measures in Vedic and Post-Vedic Era |
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25 | (1) |
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2.7 Perception of Cause and Effect as Independent and Dependent Events |
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26 | (3) |
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2.8 Development of Probabilistic Causal Algebra: Evolution of Effect as Measure of Dependence to Probabilistic Cause |
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29 | (1) |
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2.9 Emergence of Measures of Association and Dependence: Correlation and Regression Coefficients |
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30 | (1) |
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2.10 Path Coefficients, Factor Analysis and Principal Components (Karhunen--Loeve Expansion) |
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31 | (1) |
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2.11 Advancements of Concepts and Computations for Associations and Dependence |
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32 | (1) |
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2.12 Discriminant Function and Measures of Dependence |
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33 | (2) |
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2.13 The Default Correlation: Copula |
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35 | (1) |
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2.14 The Apex Vertex of Dynamism (V3) |
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35 | (1) |
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2.15 Markov Chain and Bayesian Inference |
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36 | (2) |
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2.16 The Brownian Motion---Weiner Process |
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38 | (2) |
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2.17 Stochastic Differential Equation: ITO's Process |
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40 | (7) |
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41 | (6) |
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3 Univariate Normal Distribution and Its Quantile |
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47 | (14) |
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3.1 Probability Distribution |
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47 | (2) |
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3.2 Normal Probability Distribution |
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49 | (1) |
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50 | (1) |
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3.4 Quantile and Its Role in Decision-Making |
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51 | (3) |
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3.5 Certainty Equivalent and Quantile |
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54 | (7) |
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57 | (4) |
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4 Bivariate Normal Distribution and Heuristic-Algorithm of BIVNOR for Generating Biquantile Pairs |
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61 | (30) |
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4.1 Characterization of Joint Cumulative Distribution Function |
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62 | (2) |
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4.2 Bivariate Normal Distribution: Historical Perspectives |
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64 | (2) |
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4.3 Other Properties of Bivariate Normal Distribution |
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66 | (3) |
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4.4 Owen's Computational Scheme for Evaluating Bivariate Normal Integral |
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69 | (3) |
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4.5 Other Methods for Evaluating Bivariate Normal Integral |
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72 | (1) |
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4.6 Software to Generate Tables of Bivariate Normal Quantile (Biquantile) Pairs: Prerequisite for BIVNOR |
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73 | (1) |
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4.7 Multiplicity of Biquantile Pairs: Basics of Heuristics for Developing BIVNOR |
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74 | (1) |
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4.8 Initial Steps of Heuristic BIVNOR |
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74 | (1) |
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4.9 Problems Related to Developing BIVNOR |
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75 | (1) |
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4.10 Algorithm for BIVNOR |
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75 | (6) |
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4.11 Simultaneous (Joint) Confidence Intervals |
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81 | (3) |
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4.11.1 Roy and Bose's Multivariate Confidence Bounds |
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81 | (1) |
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4.11.2 Simultaneous Confidence Interval |
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81 | (2) |
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4.11.3 Bonferroni's Interval |
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83 | (1) |
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4.11.4 Confidence Interval Based on the Chi-Square Quantile |
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84 | (1) |
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4.12 Recent Interests in Biquantile Pairs |
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84 | (3) |
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87 | (4) |
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87 | (4) |
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5 Software Reliability Testing and Tables Explained |
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91 | (12) |
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91 | (1) |
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5.2 Evolution of Reliability Testing Criteria |
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92 | (2) |
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5.3 Procedures Adopted to Meet the Evolved Criteria |
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94 | (3) |
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5.4 Generated Tables of Chaps. 8 and 9 Explained |
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97 | (6) |
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5.4.1 Description for Table 8.1 in Chap. 8: Equi-Quantile Values (or BIGH) |
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97 | (1) |
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5.4.2 Description for Table 8.2 of Chap. 8: Iso-Probable Biquantile Pairs of 400 (19 x 21 + 1 = 400) Tables |
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98 | (2) |
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5.4.3 Description of Table 9.1 of Chap. 9 (Tester Table: Owen's Table of T(h, a) Function) |
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100 | (1) |
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5.4.4 Description of Table 9.2 of Chap. 9 (Tester Tables of Biquantile Pairs for Zero Correlation Against Those for Independence Hypothesis) |
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100 | (1) |
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5.4.5 Description of Table 9.3 of Chap. 9 (Tester Tables of Iso-Probable Quantile Pairs for Random Grids of Table 8.1 of Chap. 8) |
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101 | (1) |
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102 | (1) |
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6 Decision Scenario: Problems and Prospects |
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103 | (34) |
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6.1 Decision Scenario: The Past |
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104 | (6) |
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6.2 Decision Scenario: The Present |
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110 | (1) |
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6.3 Advancements in Decision Processes: Decision Science |
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111 | (2) |
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6.4 Design of Experiment: Designing the Investigation |
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113 | (1) |
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114 | (1) |
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6.6 Discrimination and Classification |
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115 | (2) |
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6.7 Optimization: Linear Programming and Extensions |
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117 | (1) |
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6.8 Basics of Stochastic Programming and Its Chance-Constrained Version |
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118 | (5) |
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6.9 Emergence of Decision Processes Under Risk and Uncertainty |
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123 | (3) |
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123 | (1) |
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6.9.2 Von Neumann and Morgenstern versus Kahneman and Tversky |
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124 | (1) |
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6.9.3 An Attempt for Compromise |
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125 | (1) |
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6.10 Developments in Uncertain Decision-Making |
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126 | (4) |
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6.11 Online Stochastic Combinatorial Optimization |
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130 | (2) |
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132 | (5) |
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133 | (4) |
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137 | (56) |
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138 | (1) |
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7.2 Comparison Between Simultaneous (Joint) Confidence Intervals |
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138 | (9) |
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7.3 Algorithmic Heuristics for Chance-Constrained Version of Discrimination/Classification |
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147 | (4) |
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7.4 Biquantile in Optimization: Bivariate Joint Chance-Constrained Linear Programming Problem |
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151 | (6) |
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7.5 Bivariate Meteorological Prediction with Equi-quantile Pairs |
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157 | (4) |
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7.6 Equi-quantiles in Bio-statistical Studies |
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161 | (1) |
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7.7 The VaR Measure (The Value at Risk) |
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162 | (3) |
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7.8 Default Correlation: Gaussian Copula Model and Biquantile Pairs |
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165 | (2) |
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7.9 Bivariate Quality Control, Six Sigma Techniques and Biquantile Pairs |
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167 | (1) |
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7.10 Bivariate Stochastic Process and Biquantile Pairs |
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168 | (6) |
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7.11 Simulation and Biquantile Pair/Equi-quantile Value |
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174 | (3) |
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7.12 From Biquantiles to Higgs Boson (God Particle) |
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177 | (3) |
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7.13 Rizopoulos's Paradox (2009) |
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180 | (4) |
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180 | (1) |
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7.13.2 The Paradox: Its Modification and Solution |
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181 | (3) |
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184 | (1) |
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7.13.4 Reliability and Validity Tests of BIVNOR for Extreme Paradigms |
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184 | (1) |
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7.14 Further Scope for Applications of Biquantiles |
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184 | (1) |
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7.15 Information Gain and Learning |
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185 | (8) |
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7.15.1 Introduction to the Problem |
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185 | (2) |
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187 | (1) |
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188 | (1) |
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189 | (4) |
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8 Generated Tables by BIVNOR |
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193 | (428) |
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8.1 Table of BIGH the Equi-Quantile Values |
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193 | (3) |
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8.2 Contents for Table 8.2 (Table No. 8.2-1 to 400) |
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196 | (425) |
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9 Tables Generated for Software Testing |
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621 | (18) |
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9.1 The Table of COMP-T to Test Its Equivalence to OWEN's |
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621 | (1) |
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9.2 Tables for Testing BIVNOR COMP. PROB. with JNT. PROB Under Zero Correlation |
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622 | (8) |
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9.3 Tables Generated for Bivariate Normal Iso-Probable Quantile Pairs for TEST CASES |
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630 | (6) |
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9.4 Barycentric Coordinate Reading System: For Analysing Mixed Activities |
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636 | (3) |
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637 | (2) |
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639 | (6) |
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639 | (1) |
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639 | (3) |
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10.3 Caveats and Cautions |
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642 | (1) |
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10.4 The Ultimate Question |
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642 | (1) |
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10.5 Feller's Dictum and Winston's Aspiration |
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643 | (2) |
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644 | (1) |
Index |
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645 | |