Exercise 7.2 In the context of a point estimate of a feature with domain {0, 1}

with no inputs, it is possible for an agent to make a stochastic prediction with a parameter p ∈ [0, 1] such that the agent predicts 1 with probability p and predicts 0 otherwise. For each of the following error measures, give the expected error on a training set with n0 occurrences of 0 and n1 occurrences of 1 (as a function of p).

What is the value of p that minimizes the error? Is this worse or better than the prediction of Figure 7.3 (page 295)?

(a) sum of absolute errors

(b) sum-of-squares error

(c) worst-case error