$X_1$ and $X_2$ are independently distributed random variables with $$P(X_1=\Theta+1) = P(X_1=\Theta-1) = 1/2 \\ P(X_2=\Theta-2) = P(X_2=\Theta+2) = 1/2$$
- Find the values of a and b which minimize the variance of $Y=aX_1 + bX_2$ subject to the condition that $E[Y]=\Theta$.
- What is the minimum value of this variance?
The answers at the back of the book says that $a$ and $b$ is $4/5$ and $1/5$ respectively and the variance is $4/5$. I don't know how they got that answer and I'm not even sure where to start...