Question: Let T have an exponential() distribution, and conditional on T , let U be uniform on [0, T ]. (a) Express E(U |T ) and

Let T have an exponential() distribution, and conditional on T , let U be uniform on [0, T ]. (a) Express E(U |T ) and Var(U |T ) as functions of the rv T . Hint: recall the mean and variance for uniform rvs as previously derived. (b) Find the unconditional mean and variance of U by using the iterated expectation and variance partition formulas

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