On a simple fish sampling experiment, we illustrate how to take advantage of the mathematical properties of conjugate distributions. After the Beta-binomial distributions presented in Chapter 2, we now enrich the toolbox of the ecological detective with the Gamma-Normal model. No recourse to MCMC computation is needed here. We derive closedform expression of the posterior distribution of the difference between the mean lengths of two groups of fish. Rather than focusing on the complexity of the model itself, we point out the easy analytical derivation of posterior pdfs.