In probit regression, the link function is the standard normal cdf (x) = P(Z x), where

In probit regression, the link function is the standard normal cdf Φ(x) = P(Z ≤ x), where Z ~ n(0, 1). Thus, in this model we observe (Y1, x1), (V2, X2), ..., (Yn, xn), where Yi ~ Bernoulli(πi) and πi = Φ(α + βxi).
(a) Write out the likelihood function and show how to solve for the MLEs of α and β.
(b) Fit the probit model to the data of Table 12.3.1. Comment on any differences from the logistic fit.