Please send me any related solution regarding this problem please anything will be appreciated....

Problem 3. (Derivatives of characteristic functions) a Show that if X ias Ir. moments, then the characteristic function, 95X (t), is ktirnes continuously differentajble and mm) = aim! for 2 5 k. a Show that the converse is falss for odd 1' and true for even 1'. 0 Use this to give a second proof of the weak law of large numbers. (Hint: show that 96%) = 1 + 3'7? + 0(1) and then use the fact that ifan + 2 then {1 + an)\" $ ea)