Question

QUESTION 1 The length of life of an electronic component used in a guidance control system for missiles is assumed to follow a Weibull distribution with density given by >0, θ > 0 Let Yı,Y2, ,Y10 denote a random variables for the lifetime of a sample of size n= 10 of these electronic components. We wish to construct a 95% confidence interval for θ (a) Find the maximum likelihood estimator, 6, of 0. (b) Find the distribution of U = 2Y2/ (c) Use the distribution of U and the method of moment-generating functions to determine the (d) Find a pivotal forS and use it to write out an expression for a 95% confidence interval for . (e) If the lifetimes of the ten sampled electronic components (in hundreds of hours) are 0.64, 1.53, 0.73, 2.26, 2.36, 1.60, 0.16, 1.83, 1.87, 1.13, what 95% confidence interval for is obtained?

Answer 1