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#### Elements of Probability and Statistics

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Since 2012, authors of this book have been engaged in teaching of probability and statistics for international exchange students. These students are from the countries along the Belt and Road of Europe, Africa and South Asia. They have very different learning bases which make it quite difficult to find a textbook that suits them. Therefore, we prepared a lecture of probability and statistics which is the prototype of this book. We adopted the mode of content+example+exercises in this textbook.
This text was designed for a one-semester course that covers the basic topics needed for a fundamental understanding of probability and statistics. Students using this text should have the equivalent of the completion of one semester of calculus. Linear algebra would be helpful but not necessary.
This textbook contains eight chapters. The first four chapters introduce the theory of probability. Sample space, event, the basic probability, discrete and continuous random variables are illustrated with examples. The binomial, Poisson, and other useful discrete distributions are discussed. In addition, continuous distributions include the normal and exponential. In all cases, reallife scenarios are given to reveal how these distributions are used in practical problems.
Chapter 1 Classical Probability
1．1 Sample Space
1．2 Event
1．3 Counting Sample Points
1．3．1 Multiplication Rule
1．3．2 Permutations and Combinations
1．4 The Concept of Probability
1．5 The Axioms of Probability
1．6 Some Element Properties on Probability
1．7 Assignment of Probabilities
1．8 Calculating Probabilities for Unions and Complements
1．9 Conditional Probability
1．10 Independence
1．11 The Law of Total Probability
1．12 Bayes Rule
Exercises

Chapter 2 Discrete Random Variables
2．1 Random Variables
2．2 Discrete Probability Distribution
2．3 Distribution Functions for Random Variables
2．4 Expected Values
2．5 Functions of a Random Variable
2．6 Variance and Standard Deviation
Exercises

Chapter 3 Continuous Random Variables
3．1 Distribution Functions for Continuous Random Variables
3．2 Expected Values
3．3 Variance
3．4 Properties of Expected Values and Variances
Exercises

Chapter 4 Examples of Random Variables
4．1 Binomial Distribution
4．2 Properties of Binomial Distributions
4．3 Poisson Distributions
4．4 The Normal Distribution
4．5 Relationships Between Binomial and Normal Distributions
Exercises

Chapter 5 Descriptive Statistics
5．1 Measures of Central Tendency
5．2 Measures of Dispersion
5．3 Stem-and-Leaf Plot
Exercises

Chapter 6 Sampling Theory
6．1 Sampling
6．2 Random Samples， Random Numbers
6．3 Population Parameters
6．4 Sample Statistics
6．5 Sampling Distributions
6．6 The Sample Mean
6．7 Sampling Distribution of Means
6．8 Sampling Distribution of Proportions
6．9 Sampling Distribution of Differences and Sums
6．10 The Sample Variance
Exercises

Chapter 7 Estimation
7．1 Unbiased Estimates and Efficient Estimates
7．2 Point Estimates and Interval Estimates
7．3 Method of Moments
7．4 Maximum Likelihood Estimators
7．5 Confidence Interval Estimates of Population Parameters
Exercises

Chapter 8 Hypothesis Test
8．1 Statistical Hypothesis
8．2 Tests of Hypothesis
8．3 Type I and Type n Errors and Level of Significance
8．4 Simple and Composite Hypotheses
8．5 Testing Hypotheses about the Mean of a Normal Distribution with Known Variance
8．6 P Value
Exercises

Bibliography

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