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For each one of the following formulas, identify those that are always true. All integrals are...

For each one of the following formulas, identify those that are always true. All integrals are meant to be from −∞ to ∞ .

fX,Z(a,b)=∫fX,Y,Z(a′,b,c)da′

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Answer #1

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Answer: NO

If ∫fX,Y,Z(a,b,c) is the joint distribution of X, Y, Z random variables then, the marginal distribution X, Y is
fX,Y(a,b,c)=∫fX,Y,Z(a,b,c)dc

Similarly,
fX,Z(a,c)=∫fX,Y,Z(a,b,c)db

=>fX,Z(a,b)=∫fX,Y,Z(a′,b,c)da′
NO, its not always true

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