I have a homework problem about finding an optimal decision boundary. I know the formula (not really the process) for calculating one, so that may be another question entirely, but I do know I need the mean, covariance, and priors. The question is shown below
Suppose points in R^2 are being obtained from two classes, C1 and C2, both of which are well described by bivariate Gaussians with means at (0,0) and (1,3) and covariances I and 2I respectively. I is the (2x2) identity matrix. If the priors of C1 and C2 are 0.4 and 0.6 respectively, what is the ideal (i.e. Bayes Optimal) decision boundary (derive the equation for this boundary)?
I'm puzzled when it says "covariances I and 2I... I is the (2x2) identity matrix."
Is there a way to calculate a numerical value for covariance based on this information? If so, how? I've never heard it phrased this way.