- #1
pinky14
- 5
- 0
Suppose that X, Y are uncorrelated random variables which are each measurements of some unknown quantity $\mu$. Both random variables have $\mu_{X} = \mu_{Y} = \mu$, but $\sigma^2_{X} > \sigma^2_{Y}$. Determine the value of $\alpha$ in [0, 1] which will minimize the variance of the random variable W = $\alpha X +(1 - \alpha)$Y. Note that E(W) = $\mu$ for any $\alpha$ so the minimal variance α gives the “best” linear combination of X, Y to use in estimating $\mu$.