1 Introduction
2 Probability
2.1 Sample Space
2.2 Events
2.3 Probability of Events
2.4 Laws of Probability
2.5 Conditional Probability
2.6 Bayes Rule
Exercises 2
3 Random Variables
3.1 Definition of Random Variables
3.2 Discrete Random Variables
3.3 Expectation and Variance
3.4 Binomial Distribution
3.5 Poisson Distribution
Exercises 3
4 Continuous Random Variables
4.1 Continuous Random Variables
4.2 Uniform Distribution
4.3 Normal Distribution
4.4 Normal Approximation to the Binomial Distribution
4.5 Exponential Distribution
4.6 Function of Random Variables
4.7 Chebyshevs Theorem
Exercises 4
5 Random Vectors and Joint Probability Distributions
5.1 Concept of Joint Probability Distributions
5.2 Conditional Distribution
5.3 Statistical Independent
5.4 Covariance and Correlation
5.5 Law of Large Numbers and Central Limit Theorem
Exercises 5
6 Fundamental Sampling Distributions and Data Descriptions
6.1 Analysis of Data
6.2 Random Sampling
6.3 Statistics
6.4 Sample Distributions
6.5 Chi-square Distribution
6.6 Students Distribution (t-Distribution)
6.7 F-Distribution
Exercises 6
7 Estimation Problems
7.1 Point Estimation
7.2 Interval Estimation
7.3 Determination of the Sample Size
7.4 Maximum Likelihood Estimation
Exercises 7
8 Testing Hypothesis
8.1 Statistical Hypothesis:General Concepts
8.2 Testing a Statistical Hypothesis
8.3 Hypothesis Concerning Mean
8.4 Hypothesis Concerning Variance
8.5 Relationship to Confidence Interval Estimation
8.6 Tests for Proportion
8.7 Tests for Independence
8.8 Goodness-of-Fit Test
Exercises 8
9 Nonparametric Statistics
9.1 Sign Test
9.2 Rank-Sum Test
9.3 Signed-Rank Test
Exercises 9
10 Regression and Correlation
10.1 Introduction
10.2 Simple Linear Regression Equation
10.3 Parameter Estimation
10.4 Tests the Usefulness of the Linear Regression Model
10.5 Predictions
10.6 Multiple Linear Regression
10.7 Linearizable Models
10.8 Normal Correlation Model
Exercises 10
11 Analysis of Variance
11.1 Introduction
11.2 One-Way Analysis of Variance
11.3 Two-Way Analysis of Variance
Exercises 11
Answer to Exercises
Review Exercises
Appendix
References