help? this is from casella and berger(2nd edition). i've attached ex. 10.1.15 as well

Example 10.1.15 (Continuation of Example 10.1.14) Suppose now that we want to estimate the variance of the Bernoulli distribution, p(1 p). The MLE of this variance is given by 15(1 13), and an estimate of the variance of this estimator can be obtained by applying the approximation of (10.1.7). We have [311,090 -19))]2 VET (13(1 '13)) = 252 n2, 103 L(19|K) p=13 _ (1 2P)2|p=z3 n p(1-p) A =12 2 13(1-15)(1 2W n i which can be 0 if f) = %, a clear underestimate of the variance of 13(1 13). The fact that the function p(1 p) is not monotone is a cause of this problem. Using Theorem 10.1.6, we can conclude that our estimator is asymptotically efcient as long as p 75 1/2. If p = 1/2 we need to use a second-order approximation as given in Theorem 5.5.26 (see Exercise 10.10). H