2）当\(y\le\alpha\)时，\(F_Y(y)=P\{Y\le y\}=P(\emptyset)=0\);当\(y\ge \beta\)时，\(F_Y(y)=P\{Y\le y\}=P(\Omega)=1\);当\(\alpha\lt y\lt \beta\)时，\(F_Y(y)=P\{Y\le y\}=P\{g(X)\le y\}\\\qquad\;\;=\left\{\begin{array}{ll}P\{X\le h(y)\},&y=g(x)在(a,b)上单增，\\P\{X\ge h(y)\},&y=g(x)在(a,b)上单减\\\end{array}\right.\\\qquad\;\;=\left\{\begin{array}{ll}F_X(h(y)),&y=g(x)在(a,b)上单增，\\1-F_X(h(y)),&y=g(x)在(a,b)上单减.\\\end{array}\right.\)