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

[TomJerry]

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;\theta) = 2(\theta-x)/\theta for 0<x<\theta
=0 elsewhere
find the estimator for \theta by the method of moments.

 

[HallsofIvy]

The f you give is NOT a probabilty distribution. Specifically
\int_0^\theta \frac{2(\theta- x)}{\theta} dx= \theta
not 1. Is there supposed to be a \theta^2 in the denominator rather than just \theta?