Question 1.

A lifetime test is carried out on a particular type of component

A total of 10 components are observed, with failure times as follows:

5.8, 1.5, 1.2, 8, 8.3, 2.6, 7.5, 5.7, 9.3, 8.8.

The failure times are assumed to be iid Exponential with hazard rate .

Determine the maximum likelihood estimate of.

Question 2.

A lifetime test is carried out on a particular type of component

A total of 11 components are observed, with failure times observed from t = 0 until t = 40.

Ten components fail during this interval.

The respective failure times are as follows:

2.5, 7.5, 5.7, 6.5, 1, 2.1, 5.1, 3.5, 1.6, 4.8.

The failure times are assumed to be iid Exponential with hazard rate .

Determine the maximum likelihood estimate lambda.