Let Y1 and Y2 be independent random variables with Y1 ~ Norm(1, 3) and Y2 ~ Norm(2, 5). If W1 = Y1 + Y2 and W2 = 4Y1 - Y2 what is the joint distribution of W1 and W2?
I see how the mean vector is simply the variables' means, and I see the diagonal of the covariance matrix is just the variance, but according to the solution the off diagonal, which is the covariance between W1 and W2, right?, should be 2. I dont see how this can be computed without the correlation coefficient, p?
Overall the covariance matrix is [23, 2; 2, 53].
Any help much appreciated. MD