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Occasionally I stumble across formulas that use exotic letters, that I do not know how to read or pronounce or what they mean, even. Also it is hard to google for them, since there is no way of typing the letter. I searched through some Unicode tables, and the one letter that comes closest is 019D, but it is not exactly it. It is a large N but with curvy endings. I just now see it in a textbook (Mixed Effects Models in S and S-Plus, p. 8) and the formula looks about like this:

$$b \sim \mathcal N(0, \sigma^2)$$

where $\mathcal N$ is the letter in question. Based on what is written in the book, I understand that the formula specifies some distribution of random variables with zero mean, and $\sigma^2$ variance. My questions are: How would I pronounce the letter? What's its Unicode value? What does it mean?

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    $\begingroup$ This $\cal{N}$? $\endgroup$
    – postmortes
    Commented Oct 13, 2015 at 11:47
  • $\begingroup$ $b \sim \mathbb N(0,\sigma):$ b is a normal distributed random variable with the mean $0$ and the standard deviation $\sigma$ (not specified). The code is: b \sim \mathbb N(0,\sigma) $\endgroup$ Commented Oct 13, 2015 at 11:48
  • $\begingroup$ Normal distribution. $\endgroup$
    – drhab
    Commented Oct 13, 2015 at 11:48
  • $\begingroup$ Yes, @postmortes! Please tell me more about it! $\endgroup$ Commented Oct 13, 2015 at 11:49
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    $\begingroup$ detexify.kirelabs.org/classify.html can help identify unfamiliar characters in TeX \mathcal{N} $\mathcal{N}$ while shapecatcher.com does something similar with Unicode 0x1d4a9 $\unicode{x1d4a9}$ $\endgroup$
    – Henry
    Commented Oct 13, 2015 at 14:04

2 Answers 2

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The N in question is $\cal{N}$ which is a calligraphic N that $\LaTeX$ produces. You can type it yourself by putting $\cal{N}$ in your question or answer[1]. As others have also noted it denotes a normal distribution with specified mean and variance. For pronouncing it, when you're first learning about it I'd recommend saying $b \sim \cal{N}(\mu,\sigma^2)$ as "b is normally distributed with mean $\mu$ and variance $\sigma^2$" as it will reinforce the meaning and slow your thinking down to give your brain time to understand what that implies.

Later on I'd probably say "b is N of $\mu$ and $\sigma^2$" unless explaining it to someone else. Notation is there to save you time for things you already understand.

I doubt it has a Unicode value, I'm afraid, but I haven't checked. Calligraphic math symbols are more of a font thing that a unicode thing I think.

[1]: You might want to experiment with putting all the different alphabet letters in calligraphic font as well to see what they look like.

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    $\begingroup$ Unicode 0x1d4a9 $\unicode{x1d4a9}$ $\endgroup$
    – Henry
    Commented Oct 13, 2015 at 14:04
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Something like $\mathcal{N}(0,\sigma^2)$? That's the symbol for a normal distribution: https://en.wikipedia.org/wiki/Normal_distribution

The formula basically says that b is normally distributed with zero mean and variance $\sigma^2$ (to be precise: what you wrote would be variance of $\sigma$, but I assume it is a typo).

In Latex, you write it as \mathcal{N}. I am not sure about an Unicode value. I.m.o. it is simply the character N in a specific font, but not an own character, but I might be wrong.

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