Suppose (x sim Nleft(0, u^{2} ight), y sim Nleft(0, sigma^{2} ight)), and (x) is independent of (y).

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Suppose \(x \sim N\left(0, u^{2}\right), y \sim N\left(0, \sigma^{2}\right)\), and \(x\) is independent of \(y\). Given \(x+y=1\), find the MLE for \(x\).

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