  In random sequential adsorption (RSA), objects are deposited randomly,
irreversibly, and sequentially; attempts leading to an overlap with previously
deposited objects are discarded. The process continues until the system reaches
a jammed state when no further additions are possible. We analyze a class of
lattice RSA models in which landing on an empty site in a segment is allowed
when at least $b$ neighboring sites on the left and the right are unoccupied.
For the minimal model ($b=1$), we compute the full counting statistics of the
occupation number. We reduce the determination of the full counting statistics
to a Riccati equation that appears analytically solvable only when $b=1$. We
develop a perturbation procedure which, in principle, allows one to determine
cumulants consecutively, and we compute the variance of the occupation number
for all $b$.
