8.5.6 A continuous random variable X is called symmetric about c if its density f satisfies the condition f ( c - z ) = f(c+z) forall z. Showthat: (i) I f X issymmetric about c and E ( X ) exists, then E ( X ) =

c. (ii) If X is symmetric about 0, then all moments of odd order (if they exist) are equal 0.