There is a large number of books covering probability and statistics. The list below is a small segment from what is available with some commentary.

John A. Rice, Mathematical Statistics and Data Analysis, Third Edition, Brooks/Cole, 2006 A nice book to get started. It is not meant for economics students but it is not too mathematically demanding and covers most of what we will cover in class. The course will be structured around this book.

D.D. Wackerly, W. Mendenhall, R. L. Scheafer, Mathematical Statistics with Applications, Seventh Edition, Thomson, Brooks/Cole, 2008. A nice introductory course to statistics with nice examples and problems.

George. G. Roussas, A Course in Mathematical Statistics, Third Edition, Academic Press, 2012. A slightly more mathematically demanding but well organized and presented.

George Casella, Roger L. Berger, Statistical Inference, Duxbury Press, 2nd edition, 2001. A heavy going and demanding book for more ambitious students.

Takeshi Amemiya, Introduction to Statistics and Econometrics, Harvard University Press, 1994. A well organized and presented book with a view towards econometrics. It is not too demanding but covers quite a bit of ground. One more advantage is its reasonable size.

William H. Greene, Econometric Analysis, Third edition, Prentice Hall, 1997. A book meant primarily for economics students who will go on to econometrics. Nicely written but occasionally demanding because it assumes some previous knowledge.

G. Grimmett, D. Stirzaker, Probability and Random Processes, Third Edition, Oxford University Press, 2001. This is an excellent probability book with a nice introduction to martingales in section 7.7, 7.8 and Chapter 12.

D. Williams, Probability with Martingales, Cambridge University Press, 1991. A more advanced book based on measure theory that covers most you will evenr need to know about martingales.