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7. Under the conditions of Example 5.17, we know that the asymptotic variance of T(X,) is given by (T'(#))202. In some applications, it's important to choose (.) so that the asymptotic variance is free of p. Such a transformation is called a variance-stabilizing transformation. (a) If X1, X2, ..., Xn ~ Poisson (A), show that T(A) = VA is variance-stabilizing. (b) If X1, X2, ..., Xn ~ Bernoulli (p), show that r(p) = arcsin(vp) is variance-stabilizing. (c) If X1, X2, . .., Xn ~ fe where fe is supported on a subset of (0, oo) and Vare (X;) is pro- portional to E. [X] , show that T(0) = log (0) is variance-stabilizing. Name at least two familiar distributions which satisfy this property