Question
Two objects with unknown weights 1 and 2 are weighed separately on a scale and together (both placed on the scale), giving three measurements x1,
Two objects with unknown weights 1 and 2 are weighed separately on a scale and together (both placed on the scale), giving three measurements x1, x2 and x3. It is known from previous experience with the scale that measurements are independent and normally distributed about the true weights with variance 1.
We have previously shown that the MLES are 1 = (2x1 + x3 x2)/3 and 2 = (2x2+x3x1)/3 and the log likelihood is l(1, 2) = (x11)2/2(x22)2/2(x312)2/2. Consider the parameterization = (1, )T where = 2 1 and the data x1 = 15.6, x2 = 29.3 and x3 = 45.8.
a) Obtain the MLE of
b) Obtain the information matrix I(1, )
c) Obtain an approximate 95% confidence interval for
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