Question: For the logistic distribution (x) 1exp(x) 1 verify that (a) d dx(x) (x)(1(x)). (b) hlogit(x) d dx log(x) 1(x). (c) Hlogit(x)

For the logistic distribution ¤(x) Æ

¡

1Åexp(¡x)

¢¡1 verify that

(a) d dx¤(x) Ƥ(x)(1¡¤(x)).

(b) hlogit(x) Æ d dx log¤(x) Æ 1¡¤(x).

(c) Hlogit(x) Æ ¡ d2 dx2 log¤(x) Ƥ(x) (1¡¤(x)) .

(d)

¯¯

Hlogit(x)

¯¯

· 1.

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