I'm a computer science student and is fairly familiar with basic probability (calculating the probability of a event occurring, pmfs and pdfs) but I find it very difficult to grasp the concepts of advanced probability like principles of data reduction (sufficiency, likelihood principle, etc), point and interval estimation, Hypothesis testing, etc. I think it is because I fail to see the intuition behind these concepts.
I tried reading books like Statistical Inference but most of the books don't give examples (may be with some pictures would help a lot) to explain the concepts well (they do give some examples to apply the theorem but not very helpful to understand the concepts). The online lectures I looked into didn't have Advanced Probability theory. :(
My question is what are some best resources online to understand these well or any books that you would recommend i.e. Books/links that has a pictorial representation of the theorems? By pictorial representation I mean something like this for example; easily understandable.