3) Let (X, Y) denote the impact point of an artillery shell which we observe. Say we have two artillery guns whose position we know exactly. The first artillery gun, call it go has expected impact point given by (0, 0) and covariance matrix: 4 1 2 (1) The second artillery gun has its expected impact point in (1, 1) but same covariance matrix. Now, we see a new impact point: (0.5, 0.5). We now that the first gun shoots 70% of shells and second gun 30%. What is probability that it was fired by first gun? We assume the impact point to be multivariate normal. HINT: the probability that for an impact point (x, y) it is the first gun which shot on that point is given by the formula: p(x, ylgun1) . 0.7 0.7 . p(x, ylgun1)) + 0.3 . p(x, ylgun2) where for (x, y) you have to take (0.5, 0.5) and the probability p(x, ylgunl) is the probability density of a multivariate normal like gun 1, ie with expectation of gunl and covariance matrix of gun 1. So, use the formula for multivariate normal probability density