  There exist extensive studies on periodic and random perturbations of various
continuous maps investigating their dynamics. This paper presents a random
piecewise smooth map derived from a simple inductor-less switching circuit. The
bifurcation parameter is bounded and randomly selected from a stationary
distribution. Due to the stochasticity inherent in either the parameter values
or the state variable, the time evolution of the state variable cannot be
predicted at a specific time instant. We observe that the state variable
exhibits completely ergodic behavior when the minimum value of the parameter is
2.0. However, the ensemble average of the state variable converges to a fixed
value. For parameter values ranging from 2.0 to 3.5, the system demonstrates
nonchaotic behavior, and the absolute value of the Lyapunov exponent increases
monotonically with the asymmetry (ap) of the distribution from which the
bifurcation parameter values are sampled. We determine the probability density
function of the random map and verify its invariance under any initial
condition. The most noteworthy result is the disappearance of chaotic behavior
when the lower range of the distribution is varied while maintaining a fixed
upper threshold for a particular distribution, even though the nonrandom map
exhibits an array of periodic and chaotic behaviors within that range.
