Let X1, X2 ., X, represent a random sample from a Rayleigh distribution with the following pdf.nf(x; 0)/(20)x > 0(a) Determine the maximum likelihood estimator of 0.(Ex,?) / nx/ n(EX;) / 2nx/ 2nO (Ex,?) / 2nCalculate the estimate from the following n = 10 observations on vibratory stress of a turbine blade under specifiedconditions. (Round your answer to three decimal places.)17.678.719.1416.4717.695.695.2814.566.215.81(b) Determine the mle of the median of the vibratory stress distribution. [Hint: First express the median in terms of0.]o (1.38636)O 1.3863ô1.38630386301.38630

Given: fx;θ=xθe-x22θ x>0 MLE of θ θ^=∑x22n The sample values given is as follows…

Let X,, X2, . .. , X, represent a random sample from a Rayleigh distribution with the following pdf. f(x; 0) x > 0 (a) Determine the maximum likelihood estimator of 0. (Ex,?) / n (ΣΧ) / 2η x/ 2n (Ex,?) / 2n Calculate the estimate from the following n = 10 observations on vibratory stress of a turbine blade under specit conditions. (Round your answer to three decimal places.) 17.67 8.71 9.14 16.47 17.69 5.69 5.28 14.56 6.21 5.81 (b) Determine the mle of the median of the vibratory stress distribution. [Hint: First express the median in term 0.] o (1.38636) O 1.3863ô 1.38636 O (1.38636) 1.38630

Let X,, X2, . .. , X, represent a random sample from a Rayleigh distribution with the following pdf. f(x; 0) x > 0 (a) Determine the maximum likelihood estimator of 0. (Ex,?) / n (ΣΧ) / 2η x/ 2n (Ex,?) / 2n Calculate the estimate from the following n = 10 observations on vibratory stress of a turbine blade under specit conditions. (Round your answer to three decimal places.) 17.67 8.71 9.14 16.47 17.69 5.69 5.28 14.56 6.21 5.81 (b) Determine the mle of the median of the vibratory stress distribution. [Hint: First express the median in term 0.] o (1.38636) O 1.3863ô 1.38636 O (1.38636) 1.38630

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Let X1, X2 .
, X, represent a random sample from a Rayleigh distribution with the following pdf.
n
f(x; 0)
/(20)
x > 0
(a) Determine the maximum likelihood estimator of 0.
(Ex,?) / n
x/ n
(EX;) / 2n
x/ 2n
O (Ex,?) / 2n
Calculate the estimate from the following n = 10 observations on vibratory stress of a turbine blade under specified
conditions. (Round your answer to three decimal places.)
17.67
8.71
9.14
16.47
17.69
5.69
5.28
14.56
6.21
5.81
(b) Determine the mle of the median of the vibratory stress distribution. [Hint: First express the median in terms of
0.]
o (1.38636)
O 1.3863ô
1.38630
38630
1.38630

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