Consider two independent random variables X and Y . Random variable X can take only even values 0, 2, 4, . . ., and for any integer k it takes value 2k with probability P[X = 2k] = $C/4^k$ , where C is a constant. Random variable Y is a Bernoulli random variable taking values 0 and 1 only, with P[Y = 1] = 1/3. Determine the value of C, the generating functions GX(s) and GY (s), and hence find the generating function GZ(s) and the corresponding probability mass function for the random variable Z = X + Y . Explain how the probability mass function of Z could be obtained without using generating functions
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I know that you split it into two and using axiom 2 make it p(x=n)=1. – sanji Nov 04 '18 at 14:22
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Unsure how to proceed – sanji Nov 04 '18 at 14:22
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Have you done the first part already so that your question only concerns the second part (.. explain how the pmf... without using generating functions.)? – drhab Nov 04 '18 at 14:30