Q4 Three electron emitters produce electron beams with changing kinetic energies that are uniformly distributed in the ranges [3,7+45], [2,5+45], and [4,10+45] (Roundup after multiplying by f). Let Y denote the total kinetic energy produced by these electron emitters. (a) Suppose that the three beam energies are independent. Determine the mean and variance of Y . (b) Suppose that the covariance between any two beam energies is -0.5. Determine the mean and variance of Y . (c) Compare and comment on the results in parts (a) and (b).

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