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I want to estimate probability $Pr(X \leq a)$, where $X$ is a continuous random variable and $a$ is given, only based on some moments of $X$ (e.g., the first four moments, but without knowing its distribution type).

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    The question as it stands is too vague. For instance, what does 'some' mean, when you say some moments of $X$? Is X a discrete or absolutely continuous random variable or ....2012-01-12
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    @user21436 : I would take the question to mean: what range of values of $\Pr(X\le a)$ is possible given specified values of the first four moments.2017-07-05

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