Let X be a discrete random variable whose range is the set of positive integers and which
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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.
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Related Book For 
Introduction To Probability Volume 2
ISBN: 9781118123331
1st Edition
Authors: Narayanaswamy Balakrishnan, Markos V. Koutras, Konstadinos G. Politis
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