This work investigates the effects of the inputs parameters uncertainties (organs conductivities, boundary data) on the problem of electrocardiography (ECG).These inputs are very important for the construction of the torso potential for the forward problem and to reconstruct the missing electric epicardial in the case of the inverse problem. We propose a new stochastic formulation allowing to combine both sources of errors. we formulate the forward and the inverse problem to a stochastic one by considering the inputs parameters as random fields and a stochastic optimal control formulation. In order to quantify multiple independent sources of uncertainties on the forward and inverse solutions, we attribute suitable probability density functions for each randomness source, and apply stochastic finite elements based on generalized polynomial chaos method. The efficiency of this approach to solve the forward and inverse ECG problem and the usability to quantify the effect of organs conductivity and epicardial boundary data uncertainties in the torso are demonstrated through a number of numerical simulations on a 2D computational mesh of a realistic torso geometry.