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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).

JanBed
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    You can just write $x$ is normal distributed with mean $\mu$ and variance $\sigma^2$. If you like formalism, something like $x \sim \operatorname{Normal}(\mu, \sigma^2)$ or $\mathcal N(\mu, \sigma^2)$. – user251257 Aug 18 '15 at 13:04
  • A sample of one, drawn from the normally distributed population? If you want a more symbolic expression, you might write this in terms of a random number generator. – hardmath Aug 18 '15 at 13:16
  • Thank you all for the answers. If it is correct I think I will stick with notation x ~ N(mu, sigma^2) – JanBed Aug 18 '15 at 14:14
  • Since Google wasn't that good at finding this post with the search "Meaning of capital curvy / kind of cursive looking N notation mathematics", I'm going to leave this comment here to see if it helps. – jrh Dec 20 '18 at 20:38

2 Answers2

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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.

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

William Hoza
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