A first course in probability and statistics

Preface	p. vii
1 Why Statistics?	p. 1
1.1 Introduction	p. 1
1.2 Representation of Data	p. 2
2 Probability on Discrete Sample Spaces	p. 5
2.1 Introduction	p. 5
2.2 Probability	p. 6
2.3 Conditional Probability	p. 19
2.4 Independence	p. 23
2.5 Exercises	p. 24
3 Discrete Probability Distributions	p. 27
3.1 Introduction	p. 27
3.2 Discrete Random Variables	p. 27
3.3 Discrete Probability Distributions	p. 30
3.4 Probability Generating Function	p. 41
3.5 Exercises	p. 43
4 Continuous Probability Distributions	p. 45
4.1 Introduction	p. 45
4.2 Distribution Function	p. 45
4.3 Probability Density Function	p. 54
4.4 Expectation and Variance	p. 60
4.5 Moments	p. 65
4.6 Moment Generating Function	p. 68
4.7 Functions of a Random Variable	p. 71
4.8 Standard Continuous Probability Distributions	p. 77
4.9 Exercises	p. 89
5 Multivariate Probability Distributions	p. 99
5.1 Introduction	p. 99
5.2 Bivariate Probability Distributions	p. 99
5.3 Conditional Distributions	p. 109
5.4 Independence	p. 114
5.5 Expectation of a Function of a Random Vector	p. 118
5.6 Correlation and Regression	p. 123
5.7 Moment Generating Function	p. 130
5.8 Multivariate Probability Distributions	p. 134
5.9 Exercises	p. 139
6 Functions of Random Vectors	p. 147
6.1 Introduction	p. 147
6.2 Functions of Two Random Variables	p. 147
6.3 Functions of Multivariate Random Vectors	p. 159
6.4 Sampling Distributions	p. 161
6.5 Exercises	p. 174
7 Approximations to Some Probability Distributions	p. 179
7.1 Introduction	p. 179
7.2 Chebyshev's Inequality	p. 180
7.3 Weak Law of Large Numbers	p. 182
7.4 Poisson Approximation to Binomial Distribution	p. 184
7.5 Central Limit Theorem	p. 187
7.6 Normal Approximation to the Binomial Distribution	p. 189
7.7 Approximation of a Chi-square Distribution by a Normal Distribution	p. 191
7.8 Convergence of Sequences of Random Variables	p. 191
7.9 Exercises	p. 193
8 Estimation	p. 197
8.1 Introduction	p. 197
8.2 Estimation	p. 199
8.3 Some Methods of Estimation	p. 208
8.4 Cramer-Rao Inequality and Efficient Estimation	p. 218
8.5 Sufficient Statistics	p. 226
8.6 Properties of a Maximum Likelihood Estimator	p. 233
8.7 Bayes Estimation	p. 238
8.8 Estimation of a Probability Density Function	p. 241
8.9 Exercises	p. 243
9 Interval Estimation and Testing of Hypotheses	p. 247
9.1 Introduction	p. 247
9.2 Interval Estimation (Confidence Interval)	p. 248
9.3 Testing of Hypotheses	p. 255
9.4 Chi-square Tests	p. 268
9.5 Exercises	p. 278
10 Linear Regression and Correlation	p. 283
10.1 Introduction	p. 283
10.2 Simple Linear Regression Model	p. 284
10.3 Multiple Linear Regression Model	p. 296
10.4 Correlation	p. 297
10.5 Exercises	p. 299
Appendix A References	p. 303
Appendix B Answers to Selected Exercises	p. 305
Appendix C Tables	p. 307
C.l Table for Standard Normal Probability Distribution	p. 308
C.2 Table for t-Distribution	p. 310
C.3 Table for Chi-square Distribution	p. 311
C.4 Table for F-Distribution	p. 312
Index	p. 315

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