Consider p.d.f. fX (x; n, m) = k



1 + |x|

2n−m for n ∈ N, m ∈ R>0 and k is the constant of integration.

(a) Derive k. (Hint: try substituting y = x2n followed by z = (1 + y)

−1 (or combine the two).)

(b) Derive the absolute moments µr := E



|X|

r

 of fX (x; n, m) and specify when they exist.