\begin{definition}[Definition:Kurtosis]
Let $X$ be a random variable with mean $\mu$ and standard deviation $\sigma$.
Then the '''kurtosis''' of $X$, usually denoted $\alpha_4$, is defined as: 
:$\alpha_4 = \expect {\paren {\dfrac {X - \mu} \sigma}^4}$
where $\expect X$ denotes the expectation of $X$.
That is, the '''kurtosis''' of $X$ is the fourth standardized moment of $X$.
\end{definition}