Let y 1 , y 2 , , y n be a random sample of n observations from an exponential distribution with mean Derive a large sample confidence interval for Start with the pivotal statistic and show that for large samples, Z is approximately a standard normal random variable Then substitute y for in the denominator (why can you do this ) and follow the pivotal method of Example 7 6 y B Z B Vn

Question: Let y 1 , y 2 , . . . , y n be a random sample of n observations from an exponential distribution with

Let y₁, y₂, . . . , y_n be a random sample of n observations from an exponential distribution with mean β. Derive a large-sample confidence interval for β. Start with the pivotal statistic

y - B Z = B/Vn

and show that for large samples, Z is approximately a standard normal random variable. Then substitute y̅ for β in the denominator (why can you do this?) and follow the pivotal method of Example 7.6.

y - B Z = B/Vn

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