Assume that in the two-variable model Yi = fa + faXi + ui the Yi are normally and independently distributed with mean = fa + faXi and variance = a2. [See Eq. (4.3.9).] As a result, the joint probability density function of Yi, Y2,..., Yn, given the preceding mean and variance, can be written as f (Yi, Y2, ..., Yn | fa + fa Xi, a2)
But in view of the independence of the Y's, this joint probability density function can be written as a product of n individual density functions as
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