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Let x1, ..., xn be a random sample from an exponential distribution, X ~ EXP(theta).

a) If x(bar) = 17.9 with n = 50, then find a one-sided lower 95% confidence limit for theta.

b) Find a one-sided lower 95% confidence limit for P(X>t) = exp(-t/theta) where t is an arbitrary known value.

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