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For
kurtosis 4
, you can reuse
\(E[X^3] = \frac{7}{2}\)
and
\(E[X^2] = \frac{11}{5}\)
and
the alternate formulas 5.4.6
to determine
\begin{equation*} E[(X-\mu)^4] = E[X^4] - 4 \mu \cdot E[X^3] + 6 \mu^2 \cdot E[X^2] - 3 \mu^4 \end{equation*}
which is the numerator for the kurtosis.
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