A First Course in Probability and Statistics

by Rao, B. L. S. Prakasa

• ISBN13: 9789812836540
• ISBN10: 9812836543
• Format: Paperback
• Copyright: 2008-12-22
• Publisher: World Scientific Pub Co Inc

Summary

This book provides a clear exposition of the theory of probability along with applications in statistics.

Table of Contents

Preface	p. vii
Why Statistics?	p. 1
Introduction	p. 1
Representation of Data	p. 2
Probability On Discrete Sample Spaces	p. 5
Introduction	p. 5
Probability	p. 6
Conditional Probability	p. 19
Independence	p. 23
Exercises	p. 24
Discrete Probability Distributions	p. 27
Introduction	p. 27
Discrete Random Variables	p. 27
Discrete Probability Distributions	p. 30
Probability Generating Function	p. 41
Exercises	p. 43
Continuous Probability Distributions	p. 45
Introduction	p. 45
Distribution Function	p. 45
Probability Density Function	p. 54
Expectation and Variance	p. 60
Moments	p. 65
Moment Generating Function	p. 68
Functions of a Random Variable	p. 71
Standard Continuous Probability Distributions	p. 77
Exercises	p. 89
Multivariate Probability Distributions	p. 99
Introduction	p. 99
Bivariate Probability Distributions	p. 99
Conditional Distributions	p. 109
Independence	p. 114
Expectation of a Function of a Random Vector	p. 118
Correlation and Regression	p. 123
Moment Generating Function	p. 130
Multivariate Probability Distributions	p. 134
Exercises	p. 139
Functions Of Random Vectors	p. 147
Introduction	p. 147
Functions of Two Random Variables	p. 147
Functions of Multivariate Random Vectors	p. 159
Sampling Distributions	p. 161
Exercises	p. 174
Approximations To Some Probability Distributions	p. 179
Introduction	p. 179
Chebyshev's Inequality	p. 180
Weak Law of Large Numbers	p. 182
Poisson Approximation to Binomial Distribution	p. 184
Central Limit Theorem	p. 187
Normal Approximation to the Binomial Distribution	p. 189
Approximation of a Chi-square Distribution by a Normal Distribution	p. 191
Convergence of Sequences of Random Variables	p. 191
Exercises	p. 193
Estimation	p. 197
Introduction	p. 197
Estimation	p. 199
Some Methods of Estimation	p. 208
Cramer-Rao Inequality and Efficient Estimation	p. 218
Sufficient Statistics	p. 226
Properties of a Maximum Likelihood Estimator	p. 233
Bayes Estimation	p. 238
Estimation of a Probability Density Function	p. 241
Exercises	p. 243
Interval Estimation and Testing Of Hypotheses	p. 247
Introduction	p. 247
Interval Estimation (Confidence Interval)	p. 248
Testing of Hypotheses	p. 255
Chi-square Tests	p. 268
Exercises	p. 278
Linear Regression and Correlation	p. 283
Introduction	p. 283
Simple Linear Regression Model	p. 284
Multiple Linear Regression Model	p. 296
Correlation	p. 297
Exercises	p. 299
References	p. 303
Answers to Selected Exercises	p. 305
Tables	p. 307
Table for Standard Normal Probability Distribution	p. 308
Table for t-Distribution	p. 310
Table for Chi-square Distribution	p. 311
Table for F-Distribution	p. 312
Index	p. 315
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