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We develop a discrete model to account for the effects of inhomogeneities onthe redshift of photons. Using this model we compute the probabilitydistribution of the observed redshift respect to the background value,obtaining that its dispersion around the central value is proportional thesquare root of the comoving distance. This implies that data analysis shouldinclude a contribution to the total error budget which depends on the distanceof the source. Assuming large scale inhomogeneities with a power spectrum givenby primordial curvature perturbations the effect is expected to be small at lowred-shift, and to become important only at very high redshift. We then considerwhat are the general implications for the estimation of background cosmologicalparameters, giving some example for the case of quantities related to theluminosity distance such as the Hubble parameter and the cosmological constant.  The model correctly reproduces the expected stochastic properties of thepropagation of photons in inhomogeneous media and due to its computationalsimplicity it could be particularly suitable for the numerical estimation ofthe effects of inhomogeneities on cosmological observables using Montecarlomethods.

A discrete estimation of the uncertainty of the background redshift and its effects on cosmological parameters