# Solved – finding variance and expected value – multivariate case

I would like to ask you a question – I bumped into a problem that I do not know how to solve- Let \$X_1;dots;X_n\$ and \$Y_1;dots; Y_m\$, be two random samples from distributions with means \$mu_1\$
and \$mu_2\$, respectively, and with the same variance \$sigma^2\$.

I would like to know how can I calculate \$E(X-Y)\$ and \$operatorname{ Var} (X-Y)\$ – could you give me a hint?

I think that the problem is having insufficient information, would be grateful for any tips. Thanks

Contents

$$E(X-Y)= E(X) – E(Y) = mu_1 – mu_2$$ Regarding the Variance: $$Var(X−Y) = Var(X) + Var(Y) – 2* COV(X,Y) = 2sigma^2 – 2COV(X, Y)= 2sigma^2$$ Note that COV(X, Y) = 0 because the two variables are assumed independent
P.S: I am assuming $$mu_1, mu_2, sigma^2$$ are known or that you know how to estimate them. Let me know if otherwise and I will clarify further