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} = a k for k = 0, 1, .... What is the distribution...

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} = a_k
for k = 0, 1, .... What is the distribution of Z = X + Y (mod 10), their sum modulo 10?