book

Probability and Statistics

Name: Probability and Statistics
ISBN: 9789332558229

by E. Rukmangadachari, E. Keshava Reddy

April 2015

Beginner

400 pages

8h 45m

English

Pearson Education India

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Title Page
Roadmap to the Syllabus
Contents
Preface
About the Author
List of Symbols
1. Probability
1.1 Introduction1.2 Sets and Set Operations1.3 Principle of Counting1.4 Permutations and Combinations1.5 Binomial Expansion1.6 Introduction to Probability1.7 Axioms of Probability1.8 Basic Theorems1.9 Conditional Probability and Independent Events1.10 Theorem of Total Probability (or the Rule of Elimination)1-201.11 Bayes’ Theorem or Rule Exercises Multiple Choice Questions Fill in the Blanks
2. Probability Distribution
2.1 Introduction2.2 Random Variables2.3 Probability Distribution2.4 Expectation or Mean or Expected Value2.5 Variance and Standard Deviation2.6 Probability Density Functions2.7 Chebyshev’s Theorem Exercises Fill in the Blanks
3. Special Distribution
3.1 Introduction3.2 Binomial (Bernoulli) Distribution3.3 Poisson Distribution3.4 Uniform Distribution3.5 Exponential Distribution3.6 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 Introduction6.2 Statistical Hypotheses6.3 Tests of Hypotheses and Significance6.4 Type I and Type II Errors6.5 Levels of Significance6.6 Statistical Test of Hypothesis Procedure6.7 Reasoning of Statistical Test of Hypothesis6.8 Inference Concerning Two Means Exercises Fill in the Blanks
7. Tests of Significance
7.1 Introduction7.2 Test for One Mean (Small Sample)7-17.3 Test for Two Means7.4 Test of Hypothesis7.5 Analysis of r × c Tables (Contingency Tables)7-187.6 Goodness-of-Fit Test: χ2 Distribution7.7 Estimation of Proportions Exercises Fill in the Blanks
8. Curve Fitting: Regression and Correlation Analysis
8.1 Introduction8.2 Linear Regression8.3 Regression Analysis8.4 Inferences Based on Least Squares Estimation8.5 Multiple Regression8.6 Correlation Analysis8.7 Least Squares Line in Terms of Sample Variances and Covariance8.8 Standard Error of Estimate8.9 Spearman’s Rank Correlation8.10 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 ANOVA9.4 ANOVA Technique9.5 Setting Up Analysis of Variance Table9.6 Shortcut Method for One-Way ANOVA9.7 Coding Method9.8 Two-Way ANOVA9.9 ANOVA in Latin-Square DesignExercises
10. Statistical Quality Control
10.1 Properties of Control Charts10.2 Shewhart Control Charts for Measurements10.3 Shewhart Control Charts for Attributes10.4 Tolerance Limits10.5 Acceptance Sampling10.6 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

Content preview from Probability and Statistics

Appendix C

Basic Results

C.1 Exponential Function e^x

e = 2.71828 18284 (Figure C.1)

e^x e^y = e^x+y

(e^x)^y = e^xy

Figure C.1 Exponential function e^x.

C.2 Logarithm

C.2.1 Natural Logarithm

ln x is the inverse of e^x and has base e (Figure C.2) and

e^ln x = x

ln(xy) = ln x + ln y

ln(x^a) = a ln x

Figure C.2 Natural logarithm (ln x).

C.2.2 Common ...

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Probability and Statistics

by E. Rukmangadachari, E. Keshava Reddy

Appendix C