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

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

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