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Let X₁, X, be a random sample from a distribution with the following density function. 0x8-1 f(x;0)=50, 00. (4) Find MLE of 8 and its asymptotic distribution. (5) Suppose we obtain a sample of 50 observations from the underlying distribution and find that log x₁ = 52.5. Construct an approximate 95% confidence interval of 8 based on the asymptotic distribution of MLE (20.025 = 1.96, 20.05 = 1.645,20.1 = 1.28)

Let X₁, X, be a random sample from a distribution with the following density function. 0x8-1 f(x;0)=50, 00. (4) Find MLE of 8 and its asymptotic distribution. (5) Suppose we obtain a sample of 50 observations from the underlying distribution and find that log x₁ = 52.5. Construct an approximate 95% confidence interval of 8 based on the asymptotic distribution of MLE (20.025 = 1.96, 20.05 = 1.645,20.1 = 1.28)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Let X₁, X₁ be a random sample from a distribution with the following density function. f(x; 0) = 0x9-1 50 . 0<x< 5,0 >0. (4) Find MLE of 9 and its asymptotic distribution. (5) Suppose we obtain a sample of 50 observations from the underlying distribution and find that log x₁ = 52.5. Construct an approximate 95% confidence interval of 0 based on the asymptotic distribution of MLE (20.025 = 1.96, 20.05 = 1.645,20.1 = 1.28)
Transcribed Image Text:Let X₁, X₁ be a random sample from a distribution with the following density function. f(x; 0) = 0x9-1 50 . 0<x< 5,0 >0. (4) Find MLE of 9 and its asymptotic distribution. (5) Suppose we obtain a sample of 50 observations from the underlying distribution and find that log x₁ = 52.5. Construct an approximate 95% confidence interval of 0 based on the asymptotic distribution of MLE (20.025 = 1.96, 20.05 = 1.645,20.1 = 1.28)
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