$.$ Consider a two class problem with three possible actions and the following loss matrix.

Calculate the expected risk and form the correot decision rule for each action.

$2.$ State the number of parameters that need to be estimated for each of the following classification problems. Correspondingly, draw a neat figure depicting the decision boundary.

a$)$ Three class problem, where each class has a circular decision boundary $($hypothesis class is circle$)$

b$)$ Two Class problem the classes are separated by a linear boundary

c$)$ Three class problem and each class is distributed normally