Probability, statistics and random processes:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Simon & Schuster
1971
|
| Schriftenreihe: | A Simon and Schuster tech outline.
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003567516&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | 280 S. graph. Darst. |
Internformat
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| 245 | 1 | 0 | |a Probability, statistics and random processes |c Louis Maisel |
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| 490 | 0 | |a A Simon and Schuster tech outline. | |
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| 650 | 4 | |a Probabilities | |
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Datensatz im Suchindex
| _version_ | 1819377458366906368 |
|---|---|
| adam_text | TABLE OF CONTENTS
IPage
PROBABILITY
CHAPTER
1.1 Definitions of Probability 1
1.2 Permutations and Combinations 4
1.3 Additive Law of Probability 7
1.4 Conditional Probability and Multiplicative Law of Probability 11
1.5 Statistical Independence 15
1.6 Supplementary Problems 16
£L PROBABILITY DISTRIBUTIONS
Chapter
2.1 Random Variables 19
2.2 Probability Density Functions 20
2.3 Dirac Delta Function 21
2.4 Probability Density Function of a Discrete Random Variable 26
2.5 Cumulative Distribution Function , 32
2.6 Statistical Averages 34
2.7 Chebyshev s Inequality. 39
2.8 Supplementary Problems 41
O SPECIAL DISTRIBUTIONS
c * 3.1 Binomial Distribution 45
3.2 Poisson Distribution 48
3.3 Uniform Distribution 52
3.4 Sinusoidal Distribution 54
3.5 Normal Distribution 56
3.6 Rayleigh Distribution 60
3.7 Gamma Distribution 63
3.8 Beta Distribution 66
3.9 Hypergeometric Distribution 68
3.10 Supplementary Problems 69
* DERIVED AND TWO DIMENSIONAL DISTRIBUTIONS
c~ 4.1 Transformation of Variables 72
4.2 Distribution of a Linear Combination of Random Variables 75
4.3 Central Limit Theorem 81
4.4 Two Dimensional Distributions 83
4.5 Moments of Two Dimensional Distributions 85
4.6 Two Dimensional Normal Distributions 88
4.7 Supplementary Problems 92
O CHARACTERISTIC FUNCTIONS
5.1 Moment Generating Functions 94
5.2 Characteristic Functions 97
5.3 Characteristic Function of the Sum of Random Variables 103,
5.4 Supplementary Problems 107
O SAMPLING THEORY I
6.1 Estimation of the Mean and Variance 110
6.2 Sampling Distribution of the Mean: Standard Deviation Unknown 113
6.3 Confidence Intervals for the Mean 115
6.4 Confidence Intervals for the True Mean: Standard Deviation Unknown 118
6.5 Sampling Distribution of the Variance 119
6.6 Confidence Intervals for the Variance 121
6.7 Comparison of Means 124
6.8 Supplementary Problems 126
( SAMPLING THEORY II
c * 7.1 Sample Range 129
7.2 Comparison of Variance: F Test 133
7.3 Goodness of Fit Test.... 137
7.4 Contingency Tables 140
7.5 Analysis of Variance: Comparison of a Set of Means 150
7.6 Components of Variances 157
7.7 Supplementary Problems 159
O LEAST SQUARES AND CORRELATION
c 8.1 Scatter Diagrams 162
8.2 Least Mean Squares Smoothing 163
8.3 Regression Line Slope Test 171
8.4 Correlation 174
8.5 Correlation Coefficient Significance Test 178
8.6 Supplementary Problems 180
y CONTINUOUS RANDOM PROCESSES
9.1 Stationary and Ergodic Processes 183
9.2 Autocorrelation and Autocovariance 190
9.3 Properties of Autocorrelation Functions 194
9.4 Gaussian Processes 196
9.5 Linear System Relationships 200
9.6 Cross Correlation Function of Two Random Processes 202
9.7 Cross Correlation Function of Periodic and Aperiodic Functions 204
9.8 Supplementary Problems 206
TO POWER SPECTRA
CM* 10.1 Periodic and Aperiodic Functions: Fourier Series 210
10.2 Power Density Spectrum: Random Signals 219
10.3 Power Density Relationships 222
10.4 Linear System Relationships 226
10.5 Noise Bandwidth 230
10.6 Cross Power Density Spectrum 232
10.7 Supplementary Problems 235
I I DISCRETE RANDOM PROCESSES
°~ 11.1 Introduction 238
11.2 Correlation Functions 240
11.3 Linear System Relationships 245
11.4 Linear Systems with Stochastic Inputs 248
11.5 Transforms, Power and Cross Power Spectra 251
11.6 Supplementary Problems 256
STATISTICAL TABLES
TABLE I. Table of Integrals 258
TABLE II. Common Logarithms 268
TABLE III. Infinite Series 270
TABLE IV. Cumulative Normal Distribution Function 271
TABLE V. Student s f Distribution 272
TABLE VI. F Distribution for the 1 % Level of Significance 273
TABLE VII. F Distribution for the 5% Level of Significance 274
TABLE VIII. x1 Distribution 275
TABLE IX. Correlation Coefficient Test 276
INDEX 277
|
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV005710946 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T08:37:05Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003567516 |
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| physical | 280 S. graph. Darst. |
| publishDate | 1971 |
| publishDateSearch | 1971 |
| publishDateSort | 1971 |
| publisher | Simon & Schuster |
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| series2 | A Simon and Schuster tech outline. |
| spellingShingle | Maisel, Louis Sandy 1945- Probability, statistics and random processes Mathematical statistics Probabilities Stochastic processes Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4064324-4 (DE-588)4151278-9 |
| title | Probability, statistics and random processes |
| title_auth | Probability, statistics and random processes |
| title_exact_search | Probability, statistics and random processes |
| title_full | Probability, statistics and random processes Louis Maisel |
| title_fullStr | Probability, statistics and random processes Louis Maisel |
| title_full_unstemmed | Probability, statistics and random processes Louis Maisel |
| title_short | Probability, statistics and random processes |
| title_sort | probability statistics and random processes |
| topic | Mathematical statistics Probabilities Stochastic processes Statistik (DE-588)4056995-0 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Mathematical statistics Probabilities Stochastic processes Statistik Wahrscheinlichkeitsrechnung Einführung |
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