For some reason I'm finding an uniform distribution asked to be defined as a half-open interval $[0, 2)$. Either I did something wrong in doing the set calculation or then this is a form of uniform distribution.
Is it an uniform distribution? What properties does it have?
An uniform continuous distribution is one where the probability denisity function over the support interval is unbiased (ie constant).
Generally, for any $a<b$, if $X\sim \mathcal U[a;b)$ ($X$ is uniformly distributed over the interval $[a;b)$), then the pdf is $f_X(x) = \tfrac 1{b-a}\mathbf 1_{x\in[a;b)}$ and the CDF is $F_X(x)= \tfrac{x-a}{b-a}\mathbf 1_{x\in[a;b)}+\mathbf 1_{x\in[b;\infty)}$
Specifically: $X\sim \mathcal U[0;2)$ then $f_X(x) = \tfrac 12\mathbf 1_{x\in[0;2)}$ and $F_X(x)= \tfrac{x}{2}\mathbf 1_{x\in[0;2)}+\mathbf 1_{x\in[2;\infty)}$
PS: Also, an uniform discrete distribution is one where the probability mass function over the support interval is unbiased.
NB: $\mathbf 1_{x\in[a;b)}=\begin{cases} 1&:& a\leqslant x< b\\ 0 &:& \text{else}\end{cases}$