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Let U be a uniform variable on [0, 1] and let T be an independent exponential variable with a rate of 1/2. Given U =

Let U be a uniform variable on [0, 1] and let T be an independent exponential variable with a rate of 1/2.

Given U = u and T = t, let Z be a normal variable with mean u and variance t.

Find the variance of Z.

Please express your answer as a single simplified fraction.

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