Suppose you have a set of objects described by two feature values, x and y. The objects fall into two classes. Assume that they both obey a Multivariate Normal distribution. The distributions are shown below

The horizontal distribution has mean (5,0) and the vertical distribution has mean (0,5). Both distributions have the same shape but they are rotated with respect to each other. The major axis of one distribution is along the x-axis, whereas the major axis of the other distribution is along the y-axis. And the standard deviations along the major and minor axes of both distributions are 2.0 and 1.0 In the following questions please give your reasoning.

Q 5(a) Write down an equation for the Mahalanobis Distance from the horizontal distribution.

Q 5(b) Write down an equation for the Mahalanobis Distance from the vertical distribution

Q 5(c) Using Mahalanobis Distance, give an equation for the decision boundary. Try to express this equation in its simplest form.

Q 5(d) Make a sketch of the decision boundary. Show the coordinates of any points where the decision boundary crosses the x and y axes.

Q 5(e) Explain how you arrived at your sketch. You should use your equation from part (c)

The distributions are shown below al distribution has mean (5.0) and the vertic The distributions are shown below al distribution has mean (5.0) and the vertic