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28See App. A for a discussion of the normal CDF. Briefly, if a variable X follows the normal distribution with mean ^ and variance a2, its PDF is f (X) = /L= e-(X-ยป)2/2*2

and its CDF is

i-<x> V2a2n where X0 is some specified value of X.

29D. McFadden, "Conditional Logit Analysis of Qualitative Choice Behavior," in P. Zarembka (ed.), Frontiers in Econometrics, Academic Press, New York, 1973.

30A normal distribution with zero mean and unit ( = 1) variance is known as a standard or standardized normal variable (see App. A).

CHAPTER FIFTEEN: QUALITATIVE RESPONSE REGRESSION MODELS 609

where P(Y = 1 | X) means the probability that an event occurs given the value(s) of the X, or explanatory, variable(s) and where Zi is the standard normal variable, i.e., Z ~ N(0, a2). F is the standard normal CDF, which written explicitly in the present context is:

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