  An analytical expression for the spin-averaged amplitude squared of the rare
muon decay $\mu^+ \to e^+e^-e^+\nu_e\bar{\nu_\mu}$ is calculated. Monte Carlo
phase space simulation using the analytical expression for the amplitude has
been used to get various differential distributions of charged leptons. The
approximate analytical expression for the total energy spectrum of charged
leptons near the end point is presented. The dependence of branching ratio on
cuts in total energy of charged leptons is studied taking into account an
experimental energy resolution. It is shown that the measured branching ratio
is very sensitive to the energy resolution.
