Single chain AB random copolymers in a solvent which is good for B and bad for A are studied by Monte Carlo simulation. The chain statistics of the polymer coil are analyzed as a function of the number of chain beads, N, and A monomer fraction, f(e), in the regime where the chain obeys self-avoiding walk (SAW) statistics. The results are compared to a modified Flory argument [S. P. Obukhov, J. Phys. A 19, 3655 (1986)]. The argument predicts a correction to the mean radius of gyration of the coil, R(g), which scales as N--0.5 in the SAW regime. We fit the model equation to the simulations data and find good agreement. We also calculate the dispersion of R(g) as a function of f(e). We find that as f(e) is increased from f(e) = 0 to f(e) = 0.3, the dispersion of R(g) increases. Finally, we generate contours of A and B monomer density as a function of the distance from the center of mass of the chain. The contours show the emergence of an A rich region approximately the size of R(g) at the center of the coil suggesting the structure of collapsed heterogeneous macromolecules [H. S. Chan and K. A. Dill, Physics Today 2, 24 (1993)].