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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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Resultant probability distribution when taking the cosine of gaussian distributed variable

For $y=\cos(x)$, the CDF of $y$ \begin{array}{l} F_Y \left( y \right) = \left\{ {\begin{array}{*{20}l} {0,y < - 1} \\ {P\left( {2k\pi + \arccos y \le x \le 2\left( {k + 1} \right)\pi - \ar …
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