A four-point discrete distribution built from degenerate mixtures

The cumulative distribution function F of a random variable X is given by $F(x)=0.2\Delta_0(x)+0.4\Delta_1(x)+0.2\Delta_2(x)+ 0.2\Delta_3(x)$, where $\Delta_a$ is the distribution function degenerate at $a$. Consider: (I) $P(X=1\mid X\le1.5)=2/3$. (II) Variance$(X)=0$.