Q:

What does 1 with an inequality in the subscript mean?

I have not seen the following notation before (the 1 with a subscript in the density):

Consider the problem of sampling from the truncated normal
  distribution $\mathcal{N}_t (\mu, 1, a)$, given by the random variable $X ∼ \mathcal{N} (\mu, 1)$ conditional on the event $\{X \geq a\}$. Its density is proportional to
$$f(x) \propto \mathrm{exp}\{-\frac{(x-\mu)^2}{2 \sigma^2}\}1_{x \geq a}$$

What exactly does that mean?

A:

$\mathbb{1}_{x\ge a}$ is an indicator function, that is equal to $1$ when $x\ge a$ and zero otherwise. Multiplying by it is a fancy, math way of saying that everything else is equal to zero. In this case, it says that only cases greater or equal to $a$ can be observed.

A:

The I in the formula is the indicator function. In this case it equals 1 when x>=a and zero otherwise.

