Let X be a discrete random variable whose range is the set of positive integers and which has probability function

(i) Verify that this function satisfies Properties (PF1), (PF2), and (PF3) of Proposition 4.3, so that it is indeed a probability function.
(ii) Find the distribution function F(t) of the variable X.
(iii) Show that for any positive integers n, k, we have P(X > n + k|X > n) = P(X > k).
(iv) Calculate the probability that X takes on an even value.

4-3x-1 f(x)= 7t x = 1,2,3,...