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: 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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