1. Let X and Y be independent with X ~ Uniform(n) and Y~Uniform(n), and consider Z = X + Y. (a) What are the possible values of the random variable Z, and what is E(Z)? (b) Is Z uniformly distributed or are some outcomes more likely than others? Explain.
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This is because the minimum value of x and Y is 0, and the maximum value is n, so the sum can range from 0 to 2n. To find the expected value E(Z), we can use the properties of the expected value for independent random variables. Since x and Y are independent, Show more…
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