In probability theory, the arcsine distribution is the probability distribution whose cumulative distribution function involves the arcsine and the square root: F = 2 π arcsin ⁡ = arcsin ⁡ π + 1 2 {\displaystyle F={\frac {2}{\pi }}\arcsin \left={\frac {\arcsin}{\pi }}+{\frac {1}{2}}} for 0 ≤ x ≤ 1, and whose probability density function is f = 1 π x {\displaystyle f={\frac {1}{\pi {\sqrt {x}}}}} on. Wikipedia