We developed a pebble-driven core accretion model to study the formation and evolution of planets around stars in the stellar mass range of 0.08 M_⊙-1 M_⊙. By Monte Carlo sampling of the initial conditions, the growth and migration of a large number of individual protoplanetary embryos were simulated in a population synthesis manner. We tested two hypotheses for the birth locations of embryos: at the water ice line or log-uniformly distributed over entire protoplanetary disks. Two types of disks with different turbulent viscous parameters α_t of 10^-3 and 10^-4 are also investigated to shed light on the role of outward migration of protoplanets. The forming planets are compared with the observed exoplanets in terms of mass, semimajor axis, metallicity, and water content. We find that gas giant planets are likely to form when the characteristic disk sizes are larger, the disk accretion rates are higher, the disks are more metal rich, and/or their stellar hosts are more massive. Our model shows that first, the characteristic mass of super-Earth is set by the pebble isolation mass. Super-Earth masses increase linearly with the mass of its stellar host, which corresponds to one Earth mass around a late M-dwarf star and 20 Earth masses around a solar-mass star. Second, the low-mass planets, up to 20 M_⊕, can form around stars with a wide range of metallicities, while massive gas giant planets are preferred to grow around metal rich stars. Third, super-Earth planets that are mainly composed of silicates, with relatively low water fractions, can form from protoplanetary embryos at the water ice line in weakly turbulent disks where outward migration is suppressed. However, if the embryos are formed over a wide range of radial distances, the super-Earths would end up having a distinctive, bimodal composition in water mass. Altogether, our model succeeds in quantitatively reproducing several important observed properties of exoplanets and correlations with their stellar hosts.