Latent variable representation

Problem

Given:

• a random sample: \(\left( y_i,x_i \right)\) where \(y_i\) can only take values 0 or 1 and \(x_i\) is \(k×1\)

Set up the latent variable representation and derive \(P\left( y_i=1 \mid x_i \right)=x'_iβ\)