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Ŀ¼ 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¬ð 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¬ðs 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 Dtª²distribution Upper Quantiles t¦Á(n)270 Appendix E¦Ö2ª²distribution Upper Quantiles ¦Ö2¦Á(n)273 Appendix FFª²distribution Upper Quantiles F¦Á(n1,n2)276 Appendix GSome Common Probability Distributions281 Bibliography283