Consider the choice between two options, such as two product brands. Let Uy denote the utility of outcome y, for y = 0 and y = 1. Suppose Uy = ????y0 +

????y1x + ????y, using a scale such that ????y has some standardized distribution. A subject selects y = 1 if U1 > U0 for that subject.

a. If ????0 and ????1 are independent N(0, 1) random variables, show that P(y = 1)

satisfies the probit model.

b. If ????y are independent extreme-value random variables, with cdf F(????) =

exp[− exp(−????)], show that P(y = 1) satisfies the logistic regression model

(McFadden 1974).