  For the two-sided Bernoulli initial condition with density $\rho_-$ (resp.
$\rho_+$) to the left (resp. to the right), we study the distribution of a
tagged particle in the one dimensional symmetric simple exclusion process. We
obtain a formula for the moment generating function of the associated current
in terms of a Fredholm determinant. Our arguments are based on a combination of
techniques from integrable probability which have been developed recently for
studying the asymmetric exclusion process and a subsequent intricate symmetric
limit. An expression for the large deviation function of the tagged particle
position is obtained, including the case of the stationary measure with uniform
density $\rho$.
