Mathematical notation for 'value generated from normal distribution'

Question

What is the correct mathematical notation for expressing that say 'x is a value generated from the given range with the probability given by normal distribution with given mu and sigma'? I am writing a pseudoalgorithm and I need to express:

a = b + x,

where x comes from range (-inf, inf) and is picked randomly with respect to the normal distribution N(mu, sigma).

Answer 1

One often sees $$X\sim\mathcal N(\mu,\sigma^2)$$ indicating that $X$ is a random variable with the specified distribution.

In fact, I've even seen the distribution symbol itself used to stand for a quantity so distributed, e.g.,

$$\mu + \mathcal N(0,\sigma^2) =\mathcal N(\mu,\sigma^2)$$

though I don't much care for this much of a stretch of the notation.

Answer 2

You could write $x \leftarrow N(\mu, \sigma)$ to indicate the instruction "Select $x$ randomly from the distribution $N(\mu, \sigma)$."