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"Theory of Probability" by Bruno de Finetti is the best text on probability ever written.
Lindley’s Understanding Uncertainty Jaynes’s Probability Theory: The Logic of Science MacKay’s Information Theory, Inference, and Learning Algorithms ( http://www.inference.org.uk/itila/book.html )
I'm not well rounded enough to draw a clear path from where you are. For me Gelmans Data Analysis Using Regression and Multilevel/Hierarchical Models [0] drove home many, many points. More recently, I have a sense/hope that Pearl's The Book of Why [1] might take this to yet another level. [0] http://www.stat.columbia.edu/~gelman/arm/ [1] https://www.amazon.com/Book-Why-Science-Cause-Effect/dp/0465...
[0] https://en.wikipedia.org/wiki/The_Lady_Tasting_Tea
[1] https://www.johndcook.com/blog/2013/01/12/elementary-statist...
I think you will enjoy Efron & Hastie's Computer Age Statistical Inference: Algorithms, Evidence and Data Science. https://web.stanford.edu/~hastie/CASI/ MIT 6.008 Introduction to Inference also goes over many of the classic problems such as Cookie Jar, Monte Hall, Fair Dice, One-Armed Bandits, etc. with tons of labs. I find this stuff easier to grok by just writing code and running a simulation. To that end, I'd set…
But given that they distribute the PDF for free it's worth checking out. Hastie, Tibshirani & Friedman's The Elements of Statistical Learning and the watered-down and more practical Introduction to Statistical Learning are also nice. All of them can be downloaded from https://web.stanford.edu/~hastie/pub.htm
All of Statistics by Larry Wasserman is the book I recommend for anyone who knows calculus and linear algebra and wants to learn statistics.
Came here to post this and “Advanced Data Analysis from an Elementary Point of View“ by Cosmos Shalizi
There are accompanying lectures, problems, and accompanying solutions on its website https://projects.iq.harvard.edu/stat110/home