Notation doubt in probability problem

Question

My stats/probability professor handed us a bunch of exercises, and one of the last ones has this notation:

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Suppose a distribution function $F$ is given by

$$F(x) = \frac{1}{4}1_{[0,\infty)}(x) + \frac{1}{2}1_{[1,\infty)}(x) + \frac{1}{4}1_{[2,\infty)}(x)$$

Let P be given by

$$P((-\infty, x]) = F(x)$$

Find the prob. of the event $E = (\frac{2}{3}, \frac{5}{2})$

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It's my first time seing something like "$1_{[0,\infty)}(x)$", and it kind of looks like another function to me, but I don't know how to search to get what it does, could somebody tell me and how does it translates to the problem?

Thanks in advance

Answer 1

$$\Bbb 1_E(x)=\cases{1 & if $x\in E$\\0 & otherwise}$$

It's called the indicator function or characteristic function of $E$.