Suppose that the cumulative distribution function of discrete random variable $X$ is given by, $$F(x) = \begin{cases} 0 & \text{$x$ < 0 } \\[1.5ex] \dfrac{x}{4} & \text{$0 \leq x<1$}\\[1.5ex] \dfrac{1}{2}+\dfrac{x-1}{4} & \text{$1 \leq x<2$}\\[1.5ex] \dfrac{11}{12} &\text{$2 \leq x<3$}\\[1.5ex] 1 &\text{$3 \leq x$}\\ \end{cases}$$ Find $P(X=i),i=1,2,3$.
How is it possible that $X$ be a discrete random variable as I think it is a mixed random variable (both discrete and continuous) since there are $x$ in $F(X)$.
