Why two characterizations of the arcsine distribution are equiv? – math.stackexchange.com

Why two characterizations of the arcsine distribution are equiv? – math.stackexchange.com

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According to Wikipedia the CDF of arcsine dist. is: $$F(x)=\frac2{\pi}\arcsin(\sqrt{x})=\frac{\arcsin(2x-1)}{\pi}+\frac12$$ So, why are these two equivalent? Thanks in advance.

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