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For the normal distribution, which of the following is equal to 0?

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This is found by deriving, $m_X(s)$, $M_X(s)$ and $\\log(m_X(s))$ three times.

\n

By inspecting all three of these we see that only the MGF will not bring an $s$ outside the exponential during derivation and so will be the only one of these to not equal zero.

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