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Assume that $Y, Z$ are independent, zero-mean, continuous random variables with variances $\sigma_{Y}^{2}$ and $\sigma_{Z}^{2},$ respectively. Let $X=Y+Z$. The optimal value of $\alpha$ which minimizes $\mathbb{E}\left[(X-\alpha Y)^{2}\right]$ is

1. $\frac{\sigma_{Y}^{2}}{\sigma_{Y}^{2}+\sigma_{Z}^{2}}$
2. $\frac{\sigma_{Z}^{2}}{\sigma_{Y}^{2}+\sigma_{Z}^{2}}$
3. $1$
4. $\frac{\sigma_{Y}^{2}}{\sigma_{Z}^{2}}$
5. None of the above.