John E. Freund's mathematical statistics.

Content
1. Introduction
Introduction
Combinatorial Methods
Binomial Coefficients

2. Probability
Introduction
Sample spaces
Events
The Probability of an event
Some rules of Probability
etc

3. Probability Distribution and Probability Densities
introduction
Probability Distribution
Continuous Random Variables
Probability Density Functions
Multivariate Distributions
etc

4. Mathematical Expectations
Introduction
The Expected value of Random Variables
Moments
Chebyshev's Theorem
Moment- Generating Function
etc

5. Special Probability Distribution
Introduction
The Discrete Uniform Distribution
The Bernoulli Distribution
The Binomial Distribution
The Negative Binomial and Geometric Distribution
etc.

6. Special Probability Densities
Introduction
The Uniform Distribution
The Gamma, Exponential and Chi-square Distribution
The Beta Distribution
The Normal Distribution
etc

7. Functions of Random Variables
Introduction
Distribution Function Technique
Transformation Technique: One Variable
Transformation Technique: Several Variables
Moment-Generating Function Technique

8. Sampling Distributions
The Distribution of the Mean
The Distribution of the Mean: Finite Populations
The Chi-Square Distribution
The t Distribution
etc

Decision Theory
Introduction
The Theory of Games
Statistical Games
Decision Criteria
The Minimax Criteria
etc

Estimation: Theory
Introduction
Unbiased Estimator
Efficiency
Consistency
Sufficiency
etc


11. Estimation: Applications
Introduction
The estimation of Means
The estimation of Differences between Means
The estimation of proportions
The estimation of of Differences between proportions
The estimation of Variances
etc

12. Hypothesis Testing Theory
Introduction
Testing a statistical Hypothesis
Looses and Risks
The Neyman-Pearson Lemma
The power Function of a test
etc.

13. Hypothesis testing: Applications
Introduction
Tests concerning Means
Tests concerning difference between Means
Tests concerning Variances
Tests concerning Proportions
Tests concerning differences among k Proportions
etc

14. Regression and Correlation
Introduction
Linear Regression
The Method of Least squares
Normal Regression analysis
etc

15. Analysis of Variance
Introduction
One-Way Analysis of Variance
Experimental Design
Two-way analysis of Variance without interaction
Two-way analysis of Variance with interaction
etc

16. Non-parametric Test
Introduction
The sign Test
The signed -Rank Test
Ranked-Sum: Test the U test
Ranked-Sum: Test the H test
Test based on Runs
etc

Includes Index