Exercise 12.9.1. Consider the data of Example 10.3.1. Suppose a person has heart rate measurements of y = (84,82,80,69).

(a) Using normal theory linear discrimination, what is the estimated maximum likelihood allocation for this person?

(b) Using normal theory quadratic discrimination, what is the estimated maximum likelihood allocation for this person?

(c) If the two drugs have equal prior probabilities but the placebo is twice as probable as the drugs, what is the estimated maximum posterior probability allocation?

(d) Suppose the costs of correct classification are zero, the costs of misclassification depend only on the true population, and the cost of misclassifying an individual who actually has taken drug B is twice that of the other populations. Using the prior probabilities of (c), what is the estimated Bayesian allocation?

(e) What is the optimal allocation using only the first two linear discrimination coordinates?