  In this paper, we consider finitely many interval maps simultaneously acting
on the unit interval $I = [0, 1]$ in the real line $\mathbb{R}$; each with
utmost finitely many jump discontinuities and study certain important
statistical properties. Even though we use the symbolic space on $N$ letters to
reduce the case of simultaneous dynamics to maps on an appropriate space, our
aim in this paper remains to resolve ergodicity, rates of recurrence, decay of
correlations and invariance principles leading upto the central limit theorem
for the dynamics that evolves through simultaneous action. In order to achieve
our ends, we define various Ruelle operators, normalise them by various means
and exploit their spectra.
