Refer to Example 11 concerning the experiment that confirms electron antineutrinos change type. Suppose instead that there are 400 electron antineutrinos leaving the reactor. Repeat parts (a)-(c) of the example.

Data From Example 11

Transcribed Image Text:

EXAMPLE II Maximum likelihood estimator: normal distribution mean Let X1, ..., Xn be a random sample of size n from a normal distribution with known variance. Obtain the maximum likelihood estimator of . Solution Writing (x; ) = (x x + - ), the likelihood function is n L(\x1,. ,xn) = i=1 1 22 e -(xi-)/202 = e-n(x-)/20 1 - =1(xi-x)2/262 (2o)n/2 This likelihood is maximized over all values of when the exponent n(x-)/20 is minimized. Therefore, the maximum likelihood estimator = x.