6. (6+6+6+6=24 pts) Suppose that Y..... Yn are independent and identically distributed Weibull(0) random variables. That...

 

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6. (6+6+6+6=24 pts) Suppose that Y₁..... Yn are independent and identically distributed Weibull(0) random variables. That is, each Y has density function fy(yle) = 20²ye-82y2, y > 0, where > 0 is a parameter. (a) Show that the maximum likelihood estimator of is n ÔNLE= (b) Show that MLE is a sufficient statistic for the estimation of 0. (c) Find the Fisher information I(0) in a single observation from this density. (d) Using the standard approximation for the distribution of a maximum likelihood estimator based on the Fisher information, construct an approximate 99% Wald confidence interval for 0. n 2i=1 Y²* 6. (6+6+6+6=24 pts) Suppose that Y₁..... Yn are independent and identically distributed Weibull(0) random variables. That is, each Y has density function fy(yle) = 20²ye-82y2, y > 0, where > 0 is a parameter. (a) Show that the maximum likelihood estimator of is n ÔNLE= (b) Show that MLE is a sufficient statistic for the estimation of 0. (c) Find the Fisher information I(0) in a single observation from this density. (d) Using the standard approximation for the distribution of a maximum likelihood estimator based on the Fisher information, construct an approximate 99% Wald confidence interval for 0. n 2i=1 Y²*

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ANSWER STEP 1 n 6a The likelihood function for 0 L0 II fy y0 i1 28n 201 11 exp 0... View the full answer