Question: Confidence Intervals and MLE Problem 3. Let X1, ..., Xn be i.i.d. Exponential(1/0). (1) Find the MLE of 0. (2) Show that 2X1/0 has an

Confidence Intervals and MLE

Problem 3. Let X1, ..., Xn be i.i.d. Exponential(1/0). (1) Find the MLE of 0. (2) Show that 2X1/0 has an Exponential(1/2) distribution. Deduce the distribution of 2 En=] Xi/0. (3) Find the mean and variance of the MLE. (Exact calculation required). (4) Find the form of an approximate confidence interval for 0. (5) Find the form of an exact confidence interval for 0. Hint: use part (2)

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