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Generalizing the solution of Example 9.2, let the call duration T be an exponential (λ) random variable. For t0 > 0, show that the minimum mean square error estimate of T, given that T > t0, is

Example 9.2

The duration T minutes of a phonecall is an exponentialrandom variable with expected value E[T] = 3 minutes. If we observe that a call has already lasted 2 minutes, what is the minimum mean square error estimate of the call duration?

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