The following failure times of the Weibull distribution are obtained from a reliability test: 320, 370, 410, 475, 562, 613, 662, 770, 865, and 1000 hours. (a) Use the method of moments to determine...

The following failure times of the Weibull distribution are obtained from a reliability test: 320, 370, 410, 475, 562, 613, 662, 770, 865, and 1000 hours.

(a) Use the method of moments to determine the parameters that fit the above data.

(b) Use the maximum likelihood method to obtain the parameters of the Weibull distribution. Use Newton’s approach to solve for the values of the parameters. (Use γ and θ obtained from (a) as starting values for Newton’s method.)

(c) Solve (b) using the least-squares method.

(d) Compare the results obtained from (a), (b), and (c). Draw your conclusions.