statistics(inversion of ...)

1

F(x)

=0 (if x ＜1)

=∫g1(t) dt [from 1 to x] (if 1＜= x ＜2)

=∫g1(t) dt [from 1 to 2] ∫g2(t) dt [from 2 to x] (if 2＜= x ＜3)

=∫g1(t) dt [from 1 to 2] ∫g2(t) dt [from 2 to 3] ∫g3(t) dt [from 3 to x] (if 3＜= x ＜4)

=∫g1(t) dt ∫g2(t) dt [from 1 to t] ∫g3(t) dt [from 3 to 4] ∫g4(t) dt [from 4 to x] (if 4＜= x ＜5)

=1 (if 5 ＜= x)

2

f(x)

=0 (if x ＜=1)

=h1’(x) (if 1＜= x ＜=2)

=h2 ’(x) (if 2＜= x ＜=3)

=h3 ’(x) (if 3＜= x ＜=4)

=0 (if 4＜= x)