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Say we have random variable A and a bunch of random variables B_1 to B_n. All of those each independent. We also have a constant

Say we have random variable A and a bunch of random variables B_1 to B_n. All of those each independent. We also have a constant z. Now let's say we have a bunch of C_i = z*A + B_i, for every i from 0 to n. The specific kind of distributions are not known and do not matter. I wonder if we could say that the different C_i's are independent or only independent given A or neither or both

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