Among six measurement of the boiling point of a silicon compound,

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SUMMARY

The discussion centers on estimating the parameter θ for a silicon compound's boiling point using the method of moments. The error measurements provided are 0.07, 0.03, 0.14, 0.08, and 0.03 degrees Celsius. The probability density function is defined as f(x;θ) = 2(θ-x)/θ for 0 < x < θ, which does not integrate to 1, indicating it is not a valid probability distribution. The question raised concerns whether θ^2 should be in the denominator instead of θ to achieve a proper distribution.

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TomJerry
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Question:
Among six measurement of the boiling point of a silicon compound, the size of the error was 0.07,0.03,0.14,0.08 and 0.03 degree Celsius. Assuming that these data can be looked upon as a random sample from the population given by
f(x;[tex]\theta[/tex]) = 2([tex]\theta[/tex]-x)/[tex]\theta[/tex] for 0<x<[tex]\theta[/tex]
=0 elsewhere
find the estimator for [tex]\theta[/tex] by the method of moments.
 
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The f you give is NOT a probability distribution. Specifically
[tex]\int_0^\theta \frac{2(\theta- x)}{\theta} dx= \theta[/tex]
not 1. Is there supposed to be a [itex]\theta^2[/itex] in the denominator rather than just [itex]\theta[/itex]?
 

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