Maximising function
How do we maximise the function:
$$S =
\frac{\mathbb{E}[xg(x)]^2}{\mathbb{E}[xg(x)]^2(\mathbb{E}[g(x)^2]-\mathbb{E}[xg(x)]^2
+ N)+N},$$
w.r.t some arbitrary function $g(\cdot)$ that satisfies $0\leq
g(\cdot)\leq1$. When $x\in[0,\infty)$ is a positive random variable with
arbitrary density function $p(x)$ and $N$ is a constant.
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