means and covariances of random variables doubt.

Question

I am a newbie, self studying matrix algebra, and while doing the below exercise: exercise

I do struggle with the jargon/language. It says "and covariances of the random variables". I thought that to calculate covariance I need to variables $X_1$, $X_2$. Here I am just given one variable...

Anyway, what I did so far for a) is: the mean expressed as $\mu_1-2\mu_2$ and variance as $\sigma_{11}+4\sigma_{22}-4\sigma_{12}$ Is that all the answer requested? or am I missing something, is it that all a),b),c), d) form a system of linear combinations, or each exercise a), b), c),d) is individual?

Answer 1

You are given three new random variable $Y_1,Y_2,Y_3$ defined in terms of $X_1,X_2$. You have to find means of these as well as the covariances $EY_iY_j-EY_i EY_j$ for all pairs $i,j$.