The probability function of a variable X is given by

4(x-1) f(x)= 3 x Ry = {2, 3, 4, ...}. (i) Show that 2n+1 P(X > n) = n = 2,3,... 3" (ii) Verify that the variable X satisfies the inequality P(X>n+k\X>k) < P(X > k) for any nonnegative integers n, k. (Hint: Use the formulas and 00 = n=0 valid for t