Let X represent the error in making a measurement of a physical characteristic or property (e.g., the boiling point of a particular liquid). It is often reasonable to assume that E(X) = 0 and that X has a normal distribution. Thus the pdf of any particular measurement error is

(where we have used θ in place of σ2). Now suppose that n independent measurements are made, resulting in measurement errors X1 5 X1, X2 = X2, ... , Xn = Xn. Obtain the mle of θ.

1 f(x; 6) = V2ne %3D - 00