Given a univariate Gaussian with mean $\mu_1$ and variance $\sigma_1$ and a second univariate Gaussian with $\mu_2, \sigma_2$. Compare the two using the likelihood in order to find out how similar they are.
This task was given to me by my supervisor. He said "Google it, probably top hit". Now after two hours I didn't found it. I know how to compute the likelihood for some data that it was generated by some Gaussian, but not how to compare two Gaussians and he explicitly said that I should use mean and variance for both.
Edit: Not the Kullback-Leibler divergence