What does the notation $ 1_{\{x \geq 0\}}(x)$ mean?

Question

I'm taking a course on statistics and I'm not a math student so I'm not familiar with the following notation for a pdf:

$$f_X(x) =c.e^{-\lambda x}1_{\{x \geq 0\}}(x)$$

I don't get what:

$$ 1_{\{x \geq 0\}}(x)$$

means?

Answer 1

I'd write either $$ 1_{x\ge 0} $$ or $$ 1_{[0,\infty)} (x). $$ Either way, it's equal to $1$ when $x\ge 0$ and to $0$ when $x<0$.