Consider the data given in Example 4. The marginal PDF of X is obtained as follows:


EXAMPLE 5 (Continued) Likewise, the marginal PDF of Y is obtained as f (y = 3) = J2 f (x, y) = 0.27 + 0.08 + 0.16 + 0 = 0.51

x f (y = 6) = J2 f (x, y) = 0 + 0.04 + 0.10 + 0.35 = 0.49

As this example shows, to obtain the marginal PDF of X we add the column numbers, and to obtain the marginal PDF of Ywe add the row numbers. Notice that J2x f(x) over all values of Xis 1, as is J2y f (y) over all values of Y(why?).

Conditional PDF. As noted in Chapter 2, in regression analysis we are often interested in studying the behavior of one variable conditional upon the values of another variable(s). This can be done by considering the conditional PDF. The function

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