This talk will focus on the statistical characterization of cell-free massive MIMO systems. We will discuss an approximation of outage probability (OP) expressions for uplink cell-free massive multiple-input-multiple-output (CF-mMIMO) systems with and without pilot contamination. The system's access points (APs) are considered to have imperfect channel state information (CSI). The signal-to-interference-plus-noise ratio (SINR) of the CF-mMIMO system is approximated via a Log-normal distribution using a two-step moment matching method. OP and ergodic rate expressions are derived with the help of the approximated Log-normal distribution. An exact expression is first derived using conditional expectations in terms of a multi-fold integral for the no-pilot contamination scenario. Then, a novel dimension reduction method is used to approximate it by the sum of single-variable integrations. In the end, we will present the simulation results to show the utility of derived approximations.