in Probability and Statistics recategorized by
11 views
1 vote
1 vote

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.
in Probability and Statistics recategorized by
by
41.3k points
11 views

Please log in or register to answer this question.

Welcome to GO Electronics, where you can ask questions and receive answers from other members of the community.