Statistics and Probability for Engineering

Contents: 

Preface ................................................................................................ xi
What’s on the CD-ROM? ................................................................. xiii
List of Symbols .................................................................................. xv
1. Introduction: Probability and Statistics......................................... 1
1.1 Some Important Terms ................................................................... 1
1.2 What does this book contain? ....................................................... 2
2. Basic Probability ............................................................................. 6
2.1 Fundamental Concepts .................................................................. 6
2.2 Basic Rules of Combining Probabilities ......................................... 11
2.2.1 Addition Rule .................................................................... 11
2.2.2 Multiplication Rule ............................................................ 16
2.3 Permutations and Combinations .................................................. 29
2.4 More Complex Problems: Bayes’ Rule .......................................... 34
3. Descriptive Statistics: Summary Numbers ................................... 41
3.1 Central Location .......................................................................... 41
3.2 Variability or Spread of the Data ................................................... 44
3.3 Quartiles, Deciles, Percentiles, and Quantiles ................................ 51
3.4 Using a Computer to Calculate Summary Numbers ...................... 55
4. Grouped Frequencies and Graphical Descriptions ..................... 63
4.1 Stem-and-Leaf Displays ................................................................ 63
4.2 Box Plots ...................................................................................... 65
4.3 Frequency Graphs of Discrete Data .............................................. 66
4.4 Continuous Data: Grouped Frequency ......................................... 66
4.5 Use of Computers ........................................................................ 75

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5. Probability Distributions of Discrete Variables ........................... 84
5.1 Probability Functions and Distribution Functions .......................... 85
(a) Probability Functions ............................................................... 85
(b) Cumulative Distribution Functions .......................................... 86
5.2 Expectation and Variance ............................................................. 88
(a) Expectation of a Random Variable .......................................... 88
(b) Variance of a Discrete Random Variable .................................. 89
(c) More Complex Problems ......................................................... 94
5.3 Binomial Distribution ................................................................. 101
(a) Illustration of the Binomial Distribution ................................. 101
(b) Generalization of Results ...................................................... 102
(c) Application of the Binomial Distribution ............................... 102
(d) Shape of the Binomial Distribution ....................................... 104
(e) Expected Mean and Standard Deviation ................................ 105
(f) Use of Computers ................................................................ 107
(g) Relation of Proportion to the Binomial Distribution ............... 108
(h) Nested Binomial Distributions ............................................... 110
(i) Extension: Multinomial Distributions ..................................... 111
5.4 Poisson Distribution ................................................................... 117
(a) Calculation of Poisson Probabilities ....................................... 118
(b) Mean and Variance for the Poisson Distribution .................... 123
(c) Approximation to the Binomial Distribution .......................... 123
(d) Use of Computers ................................................................ 125
5.5 Extension: Other Discrete Distributions ....................................... 131
5.6 Relation Between Probability Distributions and
Frequency Distributions ............................................................... 133
(a) Comparisons of a Probability Distribution with
Corresponding Simulated Frequency Distributions ................ 133
(b) Fitting a Binomial Distribution ............................................... 135
(c) Fitting a Poisson Distribution ................................................. 136
6. Probability Distributions of Continuous Variables ................... 141
6.1 Probability from the Probability Density Function ........................ 141
6.2 Expected Value and Variance ..................................................... 149
6.3 Extension: Useful Continuous Distributions ................................ 155
6.4 Extension: Reliability ................................................................... 156

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7. The Normal Distribution............................................................. 157
7.1 Characteristics ............................................................................ 157
7.2 Probability from the Probability Density Function ........................ 158
7.3 Using Tables for the Normal Distribution .................................... 161
7.4 Using the Computer .................................................................. 173
7.5 Fitting the Normal Distribution to Frequency Data ...................... 175
7.6 Normal Approximation to a Binomial Distribution ...................... 178
7.7 Fitting the Normal Distribution to Cumulative
Frequency Data .......................................................................... 184
7.8 Transformation of Variables to Give a Normal Distribution .......... 190
8. Sampling and Combination of Variables .................................. 197
8.1 Sampling ................................................................................... 197
8.2 Linear Combination of Independent Variables ............................ 198
8.3 Variance of Sample Means ......................................................... 199
8.4 Shape of Distribution of Sample Means:
Central Limit Theorem ................................................................ 205
9. Statistical Inferences for the Mean............................................ 212
9.1 Inferences for the Mean when Variance Is Known ...................... 213
9.1.1 Test of Hypothesis ........................................................... 213
9.1.2 Confidence Interval ......................................................... 221
9.2 Inferences for the Mean when Variance Is
Estimated from a Sample ........................................................... 228
9.2.1 Confidence Interval Using the t-distribution .................... 232
9.2.2 Test of Significance: Comparing a Sample Mean
to a Population Mean ..................................................... 233
9.2.3 Comparison of Sample Means Using Unpaired Samples .. 234
9.2.4 Comparison of Paired Samples ........................................ 238
10. Statistical Inferences for Variance and Proportion ................. 248
10.1 Inferences for Variance ............................................................... 248
10.1.1 Comparing a Sample Variance with a
Population Variance ........................................................ 248
10.1.2 Comparing Two Sample Variances .................................. 252
10.2 Inferences for Proportion ........................................................... 261
10.2.1 Proportion and the Binomial Distribution ........................ 261

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10.2.2 Test of Hypothesis for Proportion .................................... 261
10.2.3 Confidence Interval for Proportion .................................. 266
10.2.4 Extension ........................................................................ 269
11. Introduction to Design of Experiments................................... 272
11.1 Experimentation vs. Use of Routine Operating Data ................... 273
11.2 Scale of Experimentation ............................................................ 273
11.3 One-factor-at-a-time vs. Factorial Design .................................... 274
11.4 Replication ................................................................................. 279
11.5 Bias Due to Interfering Factors ................................................... 279
(a) Some Examples of Interfering Factors .................................... 279
(b) Preventing Bias by Randomization ........................................ 280
(c) Obtaining Random Numbers Using Excel .............................. 284
(d) Preventing Bias by Blocking .................................................. 285
11.6 Fractional Factorial Designs ........................................................ 288
12. Introduction to Analysis of Variance ....................................... 294
12.1 One-way Analysis of Variance .................................................... 295
12.2 Two-way Analysis of Variance .................................................... 304
12.3 Analysis of Randomized Block Design ........................................ 316
12.4 Concluding Remarks .................................................................. 320
13. Chi-squared Test for Frequency Distributions ........................ 324
13.1 Calculation of the Chi-squared Function .................................... 324
13.2 Case of Equal Probabilities ......................................................... 326
13.3 Goodness of Fit .......................................................................... 327
13.4 Contingency Tables .................................................................... 331
14. Regression and Correlation ..................................................... 341
14.1 Simple Linear Regression ............................................................ 342
14.2 Assumptions and Graphical Checks ........................................... 348
14.3 Statistical Inferences ................................................................... 352
14.4 Other Forms with Single Input or Regressor ............................... 361
14.5 Correlation ................................................................................ 364
14.6 Extension: Introduction to Multiple Linear Regression ................ 367

viii
15. Sources of Further Information ............................................... 373
15.1 Useful Reference Books ............................................................. 373
15.2 List of Selected References ......................................................... 374
Appendices ...................................................................................... 375
Appendix A: Tables ............................................................................. 376
Appendix B: Some Properties of Excel Useful

Appendix C: Functions Useful Once the
During the Learning Process ....................................................... 382
Fundamentals Are Understood................................................... 386
Appendix D: Answers to Some of the Problems .................................. 387
Engineering Problem-Solver Index ............................................... 391
Index ................................................................................................ 393

Book Name: Statistics and Probability for Engineering
Edition:
Author: W.J. DeCoursey College of Engineering, University of Saskatchewan Saskatoon
Format:pdf
Type : Text/Book/Ref

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