6. (a) Show that if X is a geometric random variable, then P(X > +j | X > 1') : P(X > 3') for any positive integers 1' and j. (*) This is called the memoryless property of the geometric distribution. (Hint). For 0 m) : (P(X > 1))m for m : 1,2,... (try m : 2 rst). Let p : P(X : 1); then P(X > 1): 1 P(X : 1): 1 ;o, so that P(X > m) = (1 p)m. From this, conclude that X is a geometric random variable