A simple and conservative empirical likelihood function

Multiple measurements with an unknown Gaussian likelihood function are treated probabilistically. The likelihood function L(\mu)\propto \left( (n-1)\sigma_x^2 +n(\mu-\overline{x})^2 \right)^{-n/4} is derived where \mu is the true value, \overline{x} is the mean, and \sigma_x^2 is the variance obtained from the n measurements.