Question: For the normal distribution (x) verify that (a) hprobit(x) d dx log(x) (x) where (x) (x)/(x). (b) Hprobit(x) d2 dx2

For the normal distribution ©(x) verify that

(a) hprobit(x) Æ d dx log©(x) Æ ¸(x) where ¸(x) Æ Á(x)/©(x).

(b) Hprobit(x) Æ ¡ d2 dx2 log©(x) Æ ¸(x) (x Ÿ(x)).

Exercise 25.7

(a) Verify equations (25.6) and (25.7).

(b) Verify the assertion that H(x) È 0 implies thatHn(¯) È 0 globally in ¯.

(c) Verify the assertion that part

(b) implies that `n(¯) is globally concave in ¯.

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