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This comprehensive presentation of the basic concepts of probability theory examines both classical and modern methods. The treatment emphasizes the relationship between probability theory and mathematical analysis, and it stresses applications to statistics as well as to analysis. Topics include:
• The laws of large numbers
• Distribution and characteristic functions
• The central limit problem
• Dependence
• Random variables taking values in a normed linear space
Each chapter features worked examples in addition to problems, and bibliographical references to supplementary reading material enhance the text.
For advanced undergraduates and graduate students in mathematics.
Description
This comprehensive presentation of the basic concepts of probability theory examines both classical and modern methods. The treatment emphasizes the relationship between probability theory and mathematical analysis, and it stresses applications to statistics as well as to analysis. Topics include:
• The laws of large numbers
• Distribution and characteristic functions
• The central limit problem
• Dependence
• Random variables taking values in a normed linear space
Each chapter features worked examples in addition to problems, and bibliographical references to supplementary reading material enhance the text.
For advanced undergraduates and graduate students in mathematics.
