The estimation of metabolic fluxes for brain metabolism is important, among other things, to test the validity of different hypotheses which have been proposed in the literature. The metabolic model that we propose considers, in addition to the blood compartment, the cytosol, and mitochondria of both astrocyte and neuron, including detailed metabolic pathways. In this work we use a recently developed methodology to perform a statistical Flux Balance Analysis (FBA) for this model. The methodology recasts the problem in the form of Bayesian statistical inference and therefore can take advantage of qualitative information about brain metabolism for the simultaneous estimation of all reaction fluxes and transport rates at steady state. By a Markov Chain Monte Carlo (MCMC) sampling method, we are able to provide for each reaction flux and transport rate a distribution of possible values. The analysis of the histograms of the reaction fluxes and transport rates provides a very useful tool for assessing the validity of different hypotheses about brain energetics proposed in the literature, and facilitates the design of the pathways network that is in accordance with what is understood of the functioning of the brain. In this work, we focus on the analysis of biochemical pathways within each cell type (astrocyte and neuron) at different levels of neural activity, and we demonstrate how statistical tools can help implement various bounds suggested by experimental data.