Hi I'm currently working through past exam questions and am stuck with the following question:
Random variables $X_1$, $X_2$ and $X_3$ are identically distributed, with common mean $\mu$, common variance $\sigma^2$, and common pairwise correlation $\rho$ (i.e. $corr(X_i,X_j) =$ $\rho$ for all i $\neq$ j). Let Y = $X_1$ - $2X_2$ + $X_3$.
a) Fin the expectation and variance of Y.
b)Find the correlation between Y and $X_1$
Am I wrong in assuming that the expectation of Y would simply be $E(X_1) - E(2X_2) + E(X_3)$ given that E(X+Y)=E(X)+E(Y). Am I completely off? Any hints would be greatly appreciated.