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Suppose that X has a discrete uniform distribution on the integers 0, 1, … , 9, and Y is…

Suppose that X has a discrete uniform distribution on the integers 0, 1, … , 9, and Y is independent and has the probability distribution Pr{Y = k} = ak for k = 0, 1, …. What is the distribution of Z = X + Y (mod 10), their sum modulo 10?

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