Given a test data sample

$3$

$2$

$1$

a$)$ calculate its posterior probabilities P$(1|$x$)$ and P$(2|$x$).$

b$)$ If the risk matrix in Step $4$ is used, calculate the Bayesian risks associated with the twoclassification actions, and then

c$)$ classify this data sample based on the Bayesian risks.

$($Show your steps and immediate results.$)$