Question: Let U be a uniform variable on [0,1] and let T be an independent exponential variable with rate 12. Given U = u and T=t,

Let U be a uniform variable on [0,1] and let T be an independent exponential variable with rate 12. 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 fractions.

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