Hi @lincoln40113 Thanks for the question. I would recommend NOT memorizing them (to save shelf space in your brain!). If it helps, if it gives you any comfort, I do not have memorized either of those circled formulas. In regard to the correlation param, the text neglects to mention that the function serves to bound the correlation param in a range from 0.12 to 0.24 (such that, I think, the bottom two rows on Table 19.4 are nonsensical as the correlation cannot exceed 0.24). If you let a = [(1-exp(-50*PD)) / (1- exp(-50))], you'll notice this reduces to 0.12*a + 0.24(1-a) so that this is a weighting function between the two bounds.
Instead, what matters here (if anything) is the directional relationship between the variables, correlation and PD, and to a lessor extent the maturity adjustment. Semi-related, a recent discussion is here https://www.bionicturtle.com/forum/...re-the-global-financial-crisis-2nd-of-2.23287 because one of my quiz choices is the true/false statement "a. Under the Internal Ratings Based (IRB) approach to credit risk, default probability (PD) increases as the correlation parameter increases" ... as you know, I write deep questions, but in the 2020 review (i.e., 20.8.2. signifies a 2020 question), I was NOT going to ask for calculations here but only about the relationship. And you'll see in the thread how Evelyn asked (to me) an interesting follow-on. I hope that's helpful!