In 7 months I will have to take a "Probability" qualification exam similar to the ones shown here:
Could somebody please recommend the best textbook(s) + specific chapters that would cover all this material?
I would prefer advice from professors of mathematics or at least graduate students of mathematics.
On
Let me add my two bits worth.
Looks like a typical Ph. D. exam in social sciences where one is looking for awareness of basics of probability. That said, my recommendation would be to get a tutorial style book. I would highly recommend
Schaum's Outline of Probability and Statistics, 3/E: Edition 3 John Schiller R. Alu Srinivasan Murray Spiege
It is designed for quick study and great for self study and will be at a level you seek.
I know I am going to get into trouble for suggesting a cookbook, but trust me, the book is not as shallow as it first appears.
I am extremely surprised that those are kinds of questions that appear on PhD qualification exams. The difficulty level seems to be no harder than first or second year undergrad probability courses.
"Mathematical Statistics with Applications" by Schaeffer et al. Any book in the Duxbury series is good as an introductory textbook for probability and statistics.