An alternative latent variable model results from early applications of binary response models to toxicology studies (such as Table 5.4) of the effect of dosage of a toxin on whether a subject dies, with an unobserved tolerance distribution. For a randomly selected subject, let xi denote the dosage level and let yi = 1 if the subject dies. Suppose that the subject has a latent tolerance threshold Ti for the dosage, with (yi = 1) equivalent to (Ti ≤ xi

). Let F(t) =

P(T ≤ t).

a. For fixed dosage xi, explain why P(yi = 1 ∣ xi

) = F(xi).

b. Suppose F belongs to the normal parametric family, for some ???? and ????.

Explain why the model has the form

Φ−1(????i) = ????0 + ????1xi and relate ????0 and ????1 to ???? and ????.