Chapter 1Introduction to Probability1
1.1Random Experiments2
1.2Sample Space2
1.3Relations and Operations between Events3
1.4The Definition of Probability7
1.5Equally Likely Outcomes Model10
1.6Conditional Probability17
1.7Total Probability and Bayes Theorem20
1.8Independent Events24
Exercise 126
Chapter 2Random Variables and Distributions31
2.1Random Variables32
2.2Cumulative Distribution Function33
2.3Discrete Distributions35
2.4Some Common Discrete Distributions35
2.5Continuous Distributions41
2.6Some Useful Continuous Distributions43
2.7Functions of a Random Variable50
Exercise 256
Chapter 3Multivariate Probability Distributions61
3.1Bivariate Distributions62
3.2Marginal Distributions70
3.3Conditional Distributions73
3.4Independent Random Variables81
3.5Functions of Two or More Random Variables86
Exercise 3106
Chapter 4Characteristics of Random Variables113
4.1The Expectation of a Random Variable114
4.2Variance122
4.3The Characteristics of Some Common Distributions124
4.4Chebyshevs Inequality130
4.5Covariance and Correlation Coefficient131
4.6Moment and Covariance Matrix139
Exercise 4143
Chapter 5Large Random Samples149
5.1The Law of Large Numbers150
5.2The Central Limit Theorem152
Exercise 5156
Chapter 6Estimation159
6.1Population and Sample160
6.2Moment Estimation163
6.3Maximum Likelihood Estimation165
6.4Properties of Estimators170
6.5Three Important Distributions172
6.6Confidence Intervals182
Exercise 6191
Chapter 7Hypothesis Testing197
7.1Basics of Hypothesis Testing198
7.2Hypothesis Tests for a Population Mean200
7.3Testing Differences between Means207
7.4Hypothesis Tests for One or Two Variances210
7.5Goodness of Fit Tests214
Exercise 7219
Chapter 8Linear Regression225
8.1Linear Regression Model226
8.2Least Squares Estimation227
8.3Properties of Linear Regression Estimators230
8.4Inferences Concerning the Slope234
8.5Regression Validity236
8.6Confidence Interval for Mean Response237
8.7Inference for Prediction239
Exercise 8242
Chapter 9Introduction to R Language245
9.1Features of R Language246
9.2R Installation247
9.3Vector, Matrix and Data Frame248
9.4Loop and Branch Control Statements252
9.5Common Probability Distributions255
9.6Some Examples256
Appendix ABinomial Probability Distribution262
Appendix BPoisson Cumulative Distribution265
Appendix CStandard Normal Table268
Appendix Dtdistribution Upper Quantiles tα(n)270
Appendix Eχ2distribution Upper Quantiles χ2α(n)273
Appendix FFdistribution Upper Quantiles Fα(n1,n2)276
Appendix GSome Common Probability Distributions281
Bibliography283