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Problem 7. Consider a random sample X1, X2, Xn from the shifted exponential distribution with the following probability density function where and > 0. f(x; 0,2) = = Sle-(x-0) X ≥ 0 , (o, otherwise A random sample of ten observations provides x₁ = 3.11, x2 = 0.64, x3 = 2.55, x4 = 2.20, X5 = 5.44, x6 = 3.42, x7 = 10.39, x8 = 8.93, x9= 17.82, X10 = 1.30. 3 a. Use the method of moments to obtain estimates of 0 and λ from the random sample X1, X2, ..., Xn and compute the values of the estimates for the given data, respectively. b. Obtain the maximum likelihood estimates of 0 and λ from the random sample X1, X2, ..., Xn and compute the values of the estimates for the given data, respectively.

Problem 7. Consider a random sample X1, X2, Xn from the shifted exponential distribution with the following probability density function where and > 0. f(x; 0,2) = = Sle-(x-0) X ≥ 0 , (o, otherwise A random sample of ten observations provides x₁ = 3.11, x2 = 0.64, x3 = 2.55, x4 = 2.20, X5 = 5.44, x6 = 3.42, x7 = 10.39, x8 = 8.93, x9= 17.82, X10 = 1.30. 3 a. Use the method of moments to obtain estimates of 0 and λ from the random sample X1, X2, ..., Xn and compute the values of the estimates for the given data, respectively. b. Obtain the maximum likelihood estimates of 0 and λ from the random sample X1, X2, ..., Xn and compute the values of the estimates for the given data, respectively.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 69E
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Problem 7. Consider a random sample X1, X2, Xn from the shifted exponential distribution with the following probability density function where and > 0. f(x; 0,2) = = Sle-(x-0) X ≥ 0 , (o, otherwise A random sample of ten observations provides x₁ = 3.11, x2 = 0.64, x3 = 2.55, x4 = 2.20, X5 = 5.44, x6 = 3.42, x7 = 10.39, x8 = 8.93, x9= 17.82, X10 = 1.30. 3 a. Use the method of moments to obtain estimates of 0 and λ from the random sample X1, X2, ..., Xn and compute the values of the estimates for the given data, respectively. b. Obtain the maximum likelihood estimates of 0 and λ from the random sample X1, X2, ..., Xn and compute the values of the estimates for the given data, respectively.
Transcribed Image Text:Problem 7. Consider a random sample X1, X2, Xn from the shifted exponential distribution with the following probability density function where and > 0. f(x; 0,2) = = Sle-(x-0) X ≥ 0 , (o, otherwise A random sample of ten observations provides x₁ = 3.11, x2 = 0.64, x3 = 2.55, x4 = 2.20, X5 = 5.44, x6 = 3.42, x7 = 10.39, x8 = 8.93, x9= 17.82, X10 = 1.30. 3 a. Use the method of moments to obtain estimates of 0 and λ from the random sample X1, X2, ..., Xn and compute the values of the estimates for the given data, respectively. b. Obtain the maximum likelihood estimates of 0 and λ from the random sample X1, X2, ..., Xn and compute the values of the estimates for the given data, respectively.
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