Intermediate probability and statistics are a lot like elementary probability and statistics, but with less poncing about. Strong proficiency with calculus and linear algebra is assumed. Probability will is covered with challenging problems, classical statistics is covered in as general a fashion as can be achieved without measure theory, and a smattering of modern techniques are introduced. Intermediate probability and statistics is commonly taken by firstyear graduate students to ensure they have the necessary background to carry out statistical analysis for their experiments.
Recommended Books

Statistical Inference
George Cassella and Roger L. Berger
Key Features
 Intext exercises
 Solutions to many exercises available online
 Errata
Key Topics
 Almost Sure Convergence
 Analysis of Variance
 Asymptotic
 Common Distributions
 Conditional Probability
 Consistency and Efficiency
 Convergence in Distribution
 Convergence in Probability
 Delta Method
 Distribution and Density Functions
 Expectations of Random Variables
 Hypothesis Testing
 Interval Estimation
 Likelihood Principle
 Likelihood Ratio Testing
 Linear Regression
 Logistic Regression
 Maximum Likelihood Estimation
 Point Estimation
 Probability Theory
 Random Vectors
 Sufficiency Principle
 The Law of Large Numbers
 The Central Limit Theorem
 Transformations of Random Variables
Description
This is a standard intermediate text. It has the usual probability introduction including multivariate probability, and it covers statistical concepts including: point estimation, hypothesis testing, interval estimation, ANOVA, and regression (including logistic regression). The exposition is very clear, and the exercises are challenging. If you find yourself spending an excessive amount of time on a particular exercise, you may wish to have a look at the solution before continuing. Some of the exercises require semiheroic algebra. We heartily recommend this book; it is used for firstyear graduate courses across the country.

All of Statistics
Larry Wasserman
Key Features
 Intext exercises
 Errata
Key Topics
 Bayesian Inference
 Causal Inference
 Classification
 Conditional Probability
 Confidence Sets
 Delta Method
 Distribution and Density Functions
 Expectations of Random Variables
 Graphical Models
 Hypothesis Testing
 Important Probability Distributions
 Linear and Logistic Regression
 Maximum Likelihood Estimation
 Multivariate Distributions
 Nonparametric Curve Estimation
 Parametric Inference
 Point Estimation
 Probability
 Probability and Expectation Inequalities
 Simulation
 Smoothing
 Statistical Decision Theory
 Stochastic Processes
 The Bootstrap
 The Central Limit Theorem
 The Law of Large Numbers
 Transformations of Random Variables
Description
This book is a great statistical reference. It doesn't have the exposition and discussion of Casella & Berger, which is why it is not our top pick, but it actually contains many more statistical methods. It even offers a lot of modern methods, although it doesn't quite live up to its title. If you have sufficient mathematical maturity, you could probably use this for a first pass at intermediate statistics, but it really works better after reading a book like Cassella and Berger's.