MGF & Characteristic Functions · Statistics Graduate Level

Statistics Graduate Level Quiz

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PROBABILITY FOUNDATIONS

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Suppose

X

and

Y

are claimed to be independent,

S=X+Y

, and the characteristic functions of

X

and

S

are reported as

\phi_X(t)=e^{-2t^2}

and

\phi_S(t)=e^{-t^2}

, respectively. Which conclusion is correct?

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