For the logistic regression function in (12.3.2), verify these relationships. (a) (-/) = 1/2 (b) ((-/) + c) = 1 - ((-/) - c) for

For the logistic regression function in (12.3.2), verify these relationships.
(a) π(-α/β) = 1/2
(b) π((-α/β) + c) = 1 - π((-α/β) - c) for any c
(c) (12.3.3) for dπ(x)/dx
(d) (12.3.4) about the odds ratio
(e) (12.3.5) about the multiplicative change in odds
(f) (12.3.6) and (12.3.8) regarding the likelihood equations for a Bernoulli GLM
(g) For logistic regression, fi/(Fi(l - Fi)) = 1 in (12.3.7) and (12.3.8)