  Hierarchy of one and many-parameter families of random trigonometric chaotic
maps and one-parameter random elliptic chaotic maps of $\bf{cn}$ type with an
invariant measure have been introduced. Using the invariant measure
(Sinai-Ruelle-Bowen measure), the Kolmogrov-Sinai entropy of the random chaotic
maps have been calculated analytically, where the numerical simulations support
the results
