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Moments are summaries of random variables' characteristics (e.g., location, scale). Use also for fractional moments.
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Relation between first three moments of distribution
Consider a random variable $X$ with distribution described by the first three moments:
$$\mathbb{E}(X) = \mu$$
$$\mathbb{E}(X-\mu)^2 = \sigma^2$$
$$\mathbb{E}(X-\mu)^3 = \gamma$$
Is there a nontrivial … minimal set of assumptions or family of distributions under which the following relationship between moments holds? …