  Starting from the action-angle variables and using a standard asymptotic
expansion, here we present a new derivation of the Wave Kinetic Equation for
resonant process of the type $2\leftrightarrow 2$. Despite not offering new
physical results and despite not being more rigorous than others, our procedure
has the merit of being straightforward; it allows for a direct control of the
random phase and random amplitude hypothesis of the initial wave field. We show
that the Wave Kinetic Equation can be derived assuming only initial random
phases. The random amplitude approximation has to be taken only at the end,
after taking the weak nonlinearity and large box limits. This is because the
$\delta$-function over frequencies contains the amplitude-dependent nonlinear
correction which should be dropped before the random amplitude approximation
applies. If $\epsilon$ is the small parameter in front of the anharmonic part
of the Hamiltonian, the time scale associated with the Wave Kinetic equation is
shown to be $1/\epsilon^2$. We give evidence that random phase and amplitude
hypotheses persist up to a time of the order $1/\epsilon$.
