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Range expansion and inter-cell interference coordination (ICIC) can improve the capacity and fairness of heterogeneous network (HetNet) deployments by off-loading macrocell users to low-power nodes. Due to difficulties in analytical treatment, current studies for range expansion and ICIC in HetNets rely mostly on simulations. In this letter, first, off-loading benefits of range expansion in HetNets are captured through cumulative distribution functions (CDFs) of the downlink signal to interference plus noise ratio (SINR) difference between the macrocell and strongest picocell signals. Then, these CDFs are used to investigate the system capacity and fairness as a continuous function of the range expansion bias, and benefits of using ICIC with range expansion are demonstrated through numerical results.