5. Whereas the loss function presented in Section 16.5 supposes that a loss

(1 − p)2 is incurred when an event whose estimated probability is p occurs, another popular loss function assumes a loss of −log(p) when an event whose estimated probability is p occurs. Show that the latter loss function also has the property that if the actual (though unknown)

probability that an event occurs is α, then the expected loss when one estimates that this probability is p is minimized when p = α.