An RF compensated cylindrical Langmuir probe system has been developed and used to characterize an RF capacitive two temperature plasma discharge in a stochastic mode. The novelty of the work presented here is the use of the driven electrode (cathode) without ground shield. Measurements of the electron energy distribution function (EEDF) and plasma parameters were achieved under the following conditions: 50 W of RF power and 5×10-2 mbar of argon pressure. The probe measurements are performed at 3 cm above the electrode and the probe was shifted radially (r direction) from the center (r = 0 cm) of the inter-electrodes region towards the chamber wall (R = 10.75 cm). The results show that the EEDF is bi-Maxwellian and its shape remains the same through the scanned region. The farther the probe from the central region, the lower the EEDF maximum. The plasma density is observed to decrease according to a Gaussian profile along the radial direction and falls to 50% of its maximum when close to the cathode edge (r = 5.5 cm). At the same time the effective electron temperature remains constant for r>4 cm and increases for r>=4 cm. The high-temperature and low-temperature electrons' densities and temperatures are also discussed in the article.