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Given Problem 1) problem

To get the variance and covariance the following steps are taken: variance steps

In the step below to calculate E[Z^2] how do we approach this without a known pdf? For completeness would finding E[cos(theta)^2] be the same set of steps? But this is different because at least we know that theta has a uniform distribution? confusion

Maybe what I'm looking for is a trick, theorem or a property? I'm not completely sure how to fill my misunderstanding in this single step. Otherwise everything else in the problem makes complete sense.

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$E[Z^2] = Var(Z) + E[Z]^2 = \sigma^2 + \mu^2$

The mean and variance of Z is given in the question.

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