Question: 4. Let X, Y have the joint probability density [i x, y). Then the integral h(z) = J~ J (y - z, y) dy is

4. Let X, Y have the joint probability density [i x, y). Then the integral h(z) = J~ "J (y - z, y) dy is finite for almost all z, and is the probability density of Z= Y- X. [Since P{Z5.b}=J'!..ooh(z)dz, it is finite and hence h is finite almost everywhere.]

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