Introduction to Probability and Statistics(¸ÅÂÊͳ¼ÆÒýÂÛ)(³Â½¨Àö)

Chapter 1Introduction001
1£®1The Origin of Probability Theory and Mathematical Statistics001
1£®2Random Phenomena and Random Trials002
1£®3Statistical Regularity of Random Phenomena003
1£®4Some Important Applications of Probability and Statistics004

Chapter 2Basic Probability006
2£®1Set Theory006
2£®1£®1Sets£¬Elements£¬and Subsets006
2£®1£®2Set Operation£ºUnion£¬Intersection£¬Complement and Set Differences£¬Exclusive and Opposite008
2£®1£®3Experiments£¬Sample Spaces£¬and Events010
2£®2Set Functions011
2£®2£®1Boolean Algebras011
2£®2£®2Measures013
2£®2£®3Examples of Measures013
2£®2£®4Measures on Partitions of Sets014
2£®3Probability as Measure014
2£®3£®1Properties of Probability015
2£®4Assigning Probabilities016
2£®4£®1Classical Probability Based on Symmetry016
2£®4£®2Counting Methods for Classical Probability£ºPermutations and Combinations017
2£®4£®3Estimated Probability(Relative Frequency)019
2£®4£®4Subjective Probabilities020
2£®5Conditional Probability021
2£®5£®1Independence022
2£®5£®2The Law of Total Probability023
2£®5£®3Bayes¡¯ Theorem024
Exercises025

Chapter 3Discrete Random Variables028
3£®1Random Variables028
3£®2Probability Distributions for Discrete Random Variables030
3£®2£®1Probability Mass Function (PMF)030
3£®2£®2Cumulative Distribution Function(CDF)031
3£®2£®3Derived Distributions of Discrete Random Variables034
3£®3Some Important Discrete Probability Distributions035
3£®3£®1The Bernoulli Distribution035
3£®3£®2The Binomial Distribution036
3£®3£®3Hypergeometric Distributions037
3£®3£®4The Poisson Distribution040
3£®4Multiple Discrete Random Variables042
3£®4£®1Joint Distribution 042
3£®4£®2Marginal Distribution 044
3£®4£®3Conditional Distribution045
3£®4£®4Independence of Discrete Random Variables048
3£®4£®5Derived Distributions of Multiple Discrete Random Variables049
Exercises049

Chapter 4Continuous Random Variables054
4£®1Continuous Random Variable054
4£®1£®1Continuous Probability Distribution 054
4£®1£®2Some Important Continuous Distribution059
4£®2Multiple Continuous Random Variables066
4£®2£®1Joint Distribution066
4£®2£®2Marginal Distribution067
4£®2£®3Conditional Distribution069
4£®2£®4Independence of Continuous Random Variables070
4£®3Derived Distributions of Continuous Variable071
Exercises076

Chapter 5Numerical Characteristics of Random Variables080
5£®1Expectation080
5£®1£®1Average & Expectation080
5£®1£®2Expectations for Functions of Random Variables 082
5£®1£®3Moments of the Random Variable085
5£®2Variance 086
5£®2£®1Variance & Standard Deviation086
5£®2£®2Expectations & Variance for Several Common Distributions091
5£®3Covariance and Correlation Coefficient094
5£®3£®1Covariance and Correlation Coefficient094
5£®3£®2The Essence of Covariance and Correlation Coefficient097
Exercises100

Chapter 6Sums of Random Variables105
6£®1Sums of Independent and Identically Distributed Random Variables105
6£®2Laws of Large Numbers107
6£®2£®1Chebyshev¡¯s Inequality107
6£®2£®2The Weak Law of Large Numbers107
6£®3The Central Limit Theorem (CLT)108
6£®3£®1Example£ºSums of Exponential Random Variables109
6£®3£®2Example£ºSums of Bernoulli Random Variables£¬and the Normal Approximation to the Binomial Distribution109
Exercises111

Chapter 7Random Samples and Sampling Distributions113
7£®1Random Sampling113
7£®2Some Important Statistics115
7£®2£®1Location Measures of a Sample116
7£®2£®2Variability Measures of a Sample117
7£®3Sampling Distributions119
7£®4Some Important Sampling Distribution120
7£®4£®1Chi-square Distribution120
7£®4£®2Student¡¯s Distribution(t-Distribution)124
7£®4£®3F-distribution128
Exercises131

Chapter 8Estimation and Uncertainty133
8£®1Point Estimation133
8£®1£®1Some General Concepts of Point Estimation133
8£®1£®2Selection Criteria of Point Estimators135
8£®2Method of Point Estimation142
8£®2£®1Method of Moments142
8£®2£®2Method of Maximum Likelihood144
8£®3Interval Estimation149
8£®3£®1Basic Concepts of Confidence Intervals149
8£®3£®2Confidence Intervals for Parameters of a Normal Population151
8£®3£®3Confidence Intervals for the Difference of the Sample Means ¦Ì1-¦Ì2155
8£®4Confidence Interval for a Population Proportion p159
Exercises160

Chapter 9Hypothesis Testing164
9£®1Basic Concepts and Principles of Hypothesis Testing164
9£®1£®1Hypothesis and Test Statistic164
9£®1£®2Errors in Hypothesis Testing167
9£®2Hypotheses on a Single Normal Population168
9£®2£®1Hypothesis Concerning a Single Mean169
9£®2£®2Hypothesis Concerning a Single Variance171
9£®3Two-Sample Tests of Hypotheses 174
9£®3£®1Tests on Two Means174
9£®3£®2Tests on Two Variances177
Exercises179

Chapter 10Application of R in Probability and Statistics182
10£®1R Software Overview182
10£®1£®1Download and Installation of R Software182
10£®1£®2Using R as a Calculator183
10£®1£®3Defining and Using Variables184
10£®1£®4Vectors184
10£®1£®5Plotting Graphs185
10£®2R in Solving Probability and Statistical Problems187
10£®2£®1Probability Calculation187
10£®2£®2Plotting Statistical Graphs188
10£®2£®3Descriptive Statistics188
10£®2£®4Estimation in R190
10£®2£®5Testing Hypothesis on Mean and Variance of Normal Population195

Appendix Statistical Tables198
Table 1Poisson Distribution198
Table 2Standard Normal Distribution Function200
Table 3Values of ¦Ö2¦Á201
Table 4Values of t¦Á203
Table 5Values of F¦Á204

References210