An introduction to probability and statistical inference / George G. Roussas.

Some motivating examples and some fundamental concepts
The concept of probability and some basic results
Numerical characteristics of a random variable, some special random variables
Joint and conditional P.D.F.'s, conditional expectation and variance, moment generating function, covariance and correlation coefficient
Independence of random variables and some applications
Transformation of random variables
Some modes of convergence of random variables, applications
An overview of statistical inference
Point estimation
Confidence intervals and confidence regions
Testing hypotheses
More about testing hypotheses
A simple linear regression model
Two analysis of variance models
Some topics in nonparametric inference.