Thanks for this Rick! Very informative and thorough.

Quick question: where you show that X = ( σ exp(Y) + θ (exp(Y) + 1) ) / (exp(Y) + 1), my solution to X differs such that the "...+1" in the numerator is instead θ, as in: X = ( σ exp(Y) + θ (exp(Y) + θ) ) / (exp(Y) + 1).

Am I coming up with that incorrectly or is there a typo in your solution? When I solve for any particular X using either formula, the values are only slightly different, so I'm not sure where my error is.