Let X be continuous a random variable who's support is the entire real line and who's cumulative distribution function satisfies the initial value problem(adsbygoogle = window.adsbygoogle || []).push({});

F'(x)=s[itex]\cdot[/itex]F(x)^{a}[itex]\cdot[/itex](1-F(x))^{b}

F(m)=1/2

note that a>0, b>0, s>0 and m is real. m is the median of the distribution,

Is it possible to explicitly solve for the CDF, F(x), the PDF f(x)=F'(x), the moment or probability generating functions for X, and/or the inverse function of the CDF

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# Non Linear ODE whose solution is can be viewed as a cumulative distribution function

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