Excess Kurtosis of Student's t-Distribution
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Theorem
Let $k$ be a strictly positive integer.
Let $X \sim t_k$ where $t_k$ is the $t$-distribution with $k$ degrees of freedom.
Then the excess kurtosis $\gamma_2$ of $X$ is given by:
- $\gamma_2 = \dfrac 6 {k - 4}$
for $k > 4$, and does not exist otherwise.
Proof
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