  Let $S = S_g$ be a closed orientable surface of genus $g \geq 2$ and $Mod(S)$
be the mapping class group of $S$. In this paper, we show that the boundary
representation of $Mod(S)$ is ergodic using statistical hyperbolicity, which
generalizes the classical result of Masur on ergodicity of the action of
$Mod(S)$ on the projective measured foliation space $\mathcal{PMF}(S).$ As a
corollary, we show that the boundary representation of $Mod(S)$ is irreducible.
