Fluctuations in the vicinity of the phase transition line for two flavor QCD

We study the susceptibilities of quark number, isospin number and electric charge in numerical simulations of lattice QCD at high temperature and density. We discuss the equation of state for 2 flavor QCD at non-zero temperature and density. Derivatives of $\ln Z$ with respect to quark chemical potential $(\mu_q)$ are calculated up to sixth order. From this Taylor series, the susceptibilities are estimated as functions of temperature and $\mu_q$. Moreover, we comment on the hadron resonance gas model, which explains well our simulation results below $T_c$