4.25 ( ) Suppose we wish to approximate the logistic sigmoid (a) defined by (4.59) by a scaled probit function (a), where (a)

4.25 ( ) Suppose we wish to approximate the logistic sigmoid σ

(a) defined by (4.59)

by a scaled probit function Φ(λa), where Φ

(a) is defined by (4.114). Show that if

λ is chosen so that the derivatives of the two functions are equal at a = 0, then

λ2 = π/8.