Suppose that X and u are continuous random variables and (Xi, ui), i = 1,..., n are i.i.d.
a. Show that the joint probability density function (p.d.f.) of (ui, uj, Xi, Xj) can be written as f(ui, Xi)f(uj, Xj) for i ‰  j, where f(ui, Xi) is the joint p.d.f. of ui and Xi.
b. Show that

c. Show that

d. Show that

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