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In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.
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Orthogonal polynomials w.r.t. an arbitrary measure
Consider a random scalar variable $X$ with arbitrary measure.
I'm after a basis of polynomial functions $\{p_k\}_{k=0}^\infty$ which are orthonormal with respect to $X$ in the sense that
\begin{equati …