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Microwave and Radar Engineering
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Microwave and Radar Engineering
by E. Keshava Reddy, E. Rukmangadachari
Probability and Statistics
Title Page
Roadmap to the Syllabus
Contents
Preface
About the Author
List of Symbols
1. Probability
1.1 Introduction
1.2 Sets and Set Operations
1.3 Principle of Counting
1.4 Permutations and Combinations
1.5 Binomial Expansion
1.6 Introduction to Probability
1.7 Axioms of Probability
1.8 Basic Theorems
1.9 Conditional Probability and Independent Events
1.10 Theorem of Total Probability (or the Rule of Elimination)1-20
1.11 Bayes’ Theorem or Rule
Exercises
Multiple Choice Questions
Fill in the Blanks
2. Probability Distribution
2.1 Introduction
2.2 Random Variables
2.3 Probability Distribution
2.4 Expectation or Mean or Expected Value
2.5 Variance and Standard Deviation
2.6 Probability Density Functions
2.7 Chebyshev’s Theorem
Exercises
Fill in the Blanks
3. Special Distribution
3.1 Introduction
3.2 Binomial (Bernoulli) Distribution
3.3 Poisson Distribution
3.4 Uniform Distribution
3.5 Exponential Distribution
3.6 Normal Distribution
Exercises
Multiple Choice Questions
Fill in the Blanks
4. Sampling Distributions
4.1 Introduction
4.2 Population and Sample
4.3 Sampling Distribution
4.4 Sampling Distribution of Means (σ Known)4-3
4.5 Sampling Distribution of Proportions
4.6 Sampling Distribution of Differences and Sums
4.7 Sampling Distribution of Means (σ Unknown): t-Distribution
4.8 Chi-square (χ2) Distribution
4.9 Sampling Distribution of Variance σ 24-20
4.10 Snedecor’s F-Distribution
4.11 Fisher’s z-Distribution
Exercises
Multiple Choice Questions
Fill in the Blanks
5. Estimation Theory
5.1 Introduction
5.2 Statistical Inference
5.3 Point Estimation
5.4 Interval Estimation
5.5 Bayesian Estimation
Exercises
Fill in the Blanks
6. Inferences Concerning Means and Proportions
6.1 Introduction
6.2 Statistical Hypotheses
6.3 Tests of Hypotheses and Significance
6.4 Type I and Type II Errors
6.5 Levels of Significance
6.6 Statistical Test of Hypothesis Procedure
6.7 Reasoning of Statistical Test of Hypothesis
6.8 Inference Concerning Two Means
Exercises
Fill in the Blanks
7. Tests of Significance
7.1 Introduction
7.2 Test for One Mean (Small Sample)7-1
7.3 Test for Two Means
7.4 Test of Hypothesis
7.5 Analysis of r × c Tables (Contingency Tables)7-18
7.6 Goodness-of-Fit Test: χ2 Distribution
7.7 Estimation of Proportions
Exercises
Fill in the Blanks
8. Curve Fitting: Regression and Correlation Analysis
8.1 Introduction
8.2 Linear Regression
8.3 Regression Analysis
8.4 Inferences Based on Least Squares Estimation
8.5 Multiple Regression
8.6 Correlation Analysis
8.7 Least Squares Line in Terms of Sample Variances and Covariance
8.8 Standard Error of Estimate
8.9 Spearman’s Rank Correlation
8.10 Correlation for Bivariate Frequency Distribution
Exercises
Fill in the Blanks
9. Analysis of Variance
9.1 Analysis of Variance (ANOVA)
9.2 What is ANOVA?
9.3 The Basic Principle of ANOVA
9.4 ANOVA Technique
9.5 Setting Up Analysis of Variance Table
9.6 Shortcut Method for One-Way ANOVA
9.7 Coding Method
9.8 Two-Way ANOVA
9.9 ANOVA in Latin-Square Design
Exercises
10. Statistical Quality Control
10.1 Properties of Control Charts
10.2 Shewhart Control Charts for Measurements
10.3 Shewhart Control Charts for Attributes
10.4 Tolerance Limits
10.5 Acceptance Sampling
10.6 Two-stage Acceptance Sampling
11. Queueing Theory
11.1 Introduction
11.2 Queues or Waiting Lines
11.3 Elements of a Basic Queueing System
11.4 Description of a Queueing System
11.5 Classification of Queueing Systems
11.6 Queueing Problem
11.7 States of Queueing Theory
11.8 Probability Distribution in Queueing Systems
11.9 Kendall’s Notation for Representing Queueing Models
11.10 Basic Probabilistic Queueing Models
Exercises
Fill in the Blanks
Appendix A
Appendix B
Appendix C
Additional Solved Problems
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