Suppose we are given moments of a random variable $X$. Can we determine based on this if the random variable is continuous or not? We also assume that the moments of $X$ completely determine the distribution of $X$. In other words, do moments of continuous random variable behave fundamentally differently than moments of say discrete […]

I am trying to find a closed form or a transformation which simplify the numerical treatment of this multiple integral: $$\int_{x_1=0}^1…\int_{x_N=0}^1 \prod_r x_r^{m_r}\left(\frac {x_r f_r} {\sum_g x_g f_g}\right) ^{n_r} dx_1…dx_N $$ where $m_r$ are nonegative integers, $n_r$ are positive integers, and $f_r\ge0$ constants. There is an answer for moment $m=0$ here. Following the same exponentiation […]

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