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  • $\begingroup$ Please be careful about using "conditional on" language and notation, because many readers will understand that to mean a conditional probability, which it is not. $\endgroup$ Commented Dec 26, 2024 at 14:00
  • $\begingroup$ @whuber thank you for the hint. I attempted to clarify the statements. $\endgroup$ Commented Dec 26, 2024 at 15:46