4. The lifetime of an article is thought to have an exponential distribution. Twelve such articles...

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4. The lifetime of an article is thought to have an exponential distribution. Twelve such articles were selected at random and tested until nine of them failed. The nine observed failure times were 8, 14, 23, 32, 46, 57, 69, 88, 109. Assume that the data follow the exponential distribution (see Question 1 in Assignment 4). (a) Compute the maximum likelihood estimate of mean . (b) Compute the Fisher information for . (c) Obtain a 90% confidence interval for by using the quantity Z = ( )/se() where se() is the standard error for the estimate . 4. The lifetime of an article is thought to have an exponential distribution. Twelve such articles were selected at random and tested until nine of them failed. The nine observed failure times were 8, 14, 23, 32, 46, 57, 69, 88, 109. Assume that the data follow the exponential distribution (see Question 1 in Assignment 4). (a) Compute the maximum likelihood estimate of mean . (b) Compute the Fisher information for . (c) Obtain a 90% confidence interval for by using the quantity Z = ( )/se() where se() is the standard error for the estimate .