Page 12 - Fundamentals of Probability and Statistics for Engineers

Contents ix

6.1.2 Geometric Distribution 167
6.1.3 Negative Binomial Distribution 169
6.2 Multinomial Distribution 172
6.3 Poisson Distribution 173
6.3.1 Spatial Distributions 181
6.3.2 The Poisson Approximation to the Binomial Distribution 182
6.4 Summary 183
Further Reading 184
Problems 185
7 SOME IMPORTANT CONTINUOUS DISTRIBUTIONS 191

7.1 Uniform Distribution 191
7.1.1 Bivariate Uniform Distribution 193
7.2 Gaussian or Normal Distribution 196
7.2.1 The Central Limit Theorem 199
7.2.2 Probability Tabulations 201
7.2.3 Multivariate Normal Distribution 205
7.2.4 Sums of Normal Random Variables 207
7.3 Lognormal Distribution 209
7.3.1 Probability Tabulations 211
7.4 Gamma and Related Distributions 212
7.4.1 Exponential Distribution 215
7.4.2 Chi-Squared Distribution 219
7.5 Beta and Related Distributions 221
7.5.1 Probability Tabulations 223
7.5.2 Generalized Beta Distribution 225
7.6 Extreme-Value Distributions 226
7.6.1 Type-I Asymptotic Distributions of Extreme Values 228
7.6.2 Type-II Asymptotic Distributions of Extreme Values 233
7.6.3 Type-III Asymptotic Distributions of Extreme Values 234
7.7 Summary 238
References 238
Further Reading and Comments 238
Problems 239

PART B: STATISTICAL INFERENCE, PARAMETER
ESTIMATION, AND MODEL VERIFICATION 245

8 OBSERVED DATA AND GRAPHICAL REPRESENTATION 247
8.1 Histogram and Frequency Diagrams 248
References 252
Problems 253

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