Find cumulative distribution function of uniform distribution

Question

Random variable X has uniform distribution on $[0,1] \cup [2,3]$. Find cdf of variable X. I mean i do not know how to treat this on such strange interval.

Answer 1

For $x<0$, $F_X(x) = 0$,

For $0 \le x < 1$, $F_X(x) = x/2$,

For $1 \le x < 2$, $F_X(x) = 1/2$,

For $2 \le x < 3$, $F_X(x) = 1/2 + (x-2)/2$,

For $x \ge 3$, $F_X(x) = 1$.

Answer 2

Hint: The density function is $$f_X(x)=\begin{cases}0, & x<0 \\ 1/2, & 0\leq x \leq 1\\ 0, & 1<x<2\\ 1/2, & 2\leq x \leq 3\\ 0,x>3 \end{cases} $$

Answer 3

Hint:

$F(x)=\frac12.\text{length of }(-\infty,x]\cap([0,1]\cup[2,3])$

Discern cases.

Formally "length of" means here "the Lebesguemeasure of".