  We show that if $G$ is a non-elementary word hyperbolic group, mapping class
group of a hyperbolic surface or the outer automorphism group of a nonabelian
free group then $G$ has $2^{\aleph_0}$ many continuous ergodic invariant random
subgroups. If $G$ is a nonabelian free group then $G$ has $2^{\aleph_0}$ many
continuous $G$-ergodic characteristic random subgroups. We also provide a
complete classification of characteristic random subgroups of free abelian
groups of countably infinite rank and elementary $p$-groups of countably
infinite rank.
