We analyse the fluctuations of electric variables in a simple case of semi-infinite electrolyte solution bound by a neutral hard wall. We use the statistical field theory with the effective Hamiltonian that yields the Debye-Huckel theory in the bulk. Although there is no profile for the average electrical quantities the fluctuations are influenced by the presence of the hard wall. We have calculated the profile for the electrical potential fluctuation at a given point across the interface. Analytic expression for the charge-charge and potential-potential correlation function is given. Some perspectives for a further study on the electric variables fluctuations in inhomogeneous electrolyte systems are presented.