a) If f(x) is the probability density function (pdf) of a continuous random variable X,
what two conditions must be satised ?
(b) Hence for xed > 1, determine the constant c required to make f(x) = c=x2;
1 < x < and f(x) = 0 otherwise, a proper pdf.
(c) Suppose instead, f(x) = c=x2 ; x > with f(x) = 0 otherwise.
(i) Show that c = makes this a proper pdf.
(ii) Show that the moment generating function (mgf) does NOT exist.