Let X₁, X₂, X, represent a random sample from a Rayleigh distribution with the following pdf. =e-x²/(20) f(x; 8) = (a) Determine the maximum likelihood estimator of 0. Ο (ΣΧ.) / 2η Ox/n Ox/2n Ⓒ (EX,²)/n (EX 2)/2n X>0 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.) 12.22 10.64 7.68 8.39 11.97 17.94 5.84 17.00 7.81 14.26 (b) Determine the mle of the median of the vibratory stress distribution. [Hint: First express the median in terms of 0.] OV1.38630 1.38638 (1.38636)2 O√1.38638 (1.38636)³
Let X₁, X₂, X, represent a random sample from a Rayleigh distribution with the following pdf. =e-x²/(20) f(x; 8) = (a) Determine the maximum likelihood estimator of 0. Ο (ΣΧ.) / 2η Ox/n Ox/2n Ⓒ (EX,²)/n (EX 2)/2n X>0 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.) 12.22 10.64 7.68 8.39 11.97 17.94 5.84 17.00 7.81 14.26 (b) Determine the mle of the median of the vibratory stress distribution. [Hint: First express the median in terms of 0.] OV1.38630 1.38638 (1.38636)2 O√1.38638 (1.38636)³
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![Let \( X_1, X_2, \ldots, X_n \) represent a random sample from a Rayleigh distribution with the following probability density function (pdf):
\[ f(x; \theta) = \frac{x}{\theta} e^{-x^2/(2\theta)}, \quad x > 0 \]
**(a) Determine the maximum likelihood estimator of \( \theta \).**
- \( (\Sigma x_i^2) / 2n \)
- \( \bar{x} / n \)
- \( \bar{x} / 2n \)
- \( (\Sigma x_i^2) / n \)
- \( (\Sigma x_i^2) / 2n \)
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.)
\[
\begin{array}{cccc}
12.22 & 10.64 & 7.68 & 8.39 & 11.97 \\
17.94 & 5.84 & 17.00 & 7.81 & 14.26 \\
\end{array}
\]
**(b) Determine the MLE of the median of the vibratory stress distribution.**
\[ \text{[Hint: First express the median in terms of } \theta. \text{]} \]
- \( \sqrt{1.3863\hat{\theta}} \)
- \( 1.3863\hat{\theta} \)
- \( (1.3863\hat{\theta})^2 \)
- \( \sqrt{1.3863\hat{\theta}} \)
- \( (1.3863\hat{\theta})^3 \)
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Transcribed Image Text:Let \( X_1, X_2, \ldots, X_n \) represent a random sample from a Rayleigh distribution with the following probability density function (pdf):
\[ f(x; \theta) = \frac{x}{\theta} e^{-x^2/(2\theta)}, \quad x > 0 \]
**(a) Determine the maximum likelihood estimator of \( \theta \).**
- \( (\Sigma x_i^2) / 2n \)
- \( \bar{x} / n \)
- \( \bar{x} / 2n \)
- \( (\Sigma x_i^2) / n \)
- \( (\Sigma x_i^2) / 2n \)
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.)
\[
\begin{array}{cccc}
12.22 & 10.64 & 7.68 & 8.39 & 11.97 \\
17.94 & 5.84 & 17.00 & 7.81 & 14.26 \\
\end{array}
\]
**(b) Determine the MLE of the median of the vibratory stress distribution.**
\[ \text{[Hint: First express the median in terms of } \theta. \text{]} \]
- \( \sqrt{1.3863\hat{\theta}} \)
- \( 1.3863\hat{\theta} \)
- \( (1.3863\hat{\theta})^2 \)
- \( \sqrt{1.3863\hat{\theta}} \)
- \( (1.3863\hat{\theta})^3 \)
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