# Math formula with $\mathcal N$ symbol. What is it?

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?

• This $\cal{N}$? Commented Oct 13, 2015 at 11:47
• $b \sim \mathbb N(0,\sigma):$ 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) Commented Oct 13, 2015 at 11:48
• Normal distribution. Commented Oct 13, 2015 at 11:48
• Yes, @postmortes! Please tell me more about it! Commented Oct 13, 2015 at 11:49
• 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 $\unicode{x1d4a9}$ Commented Oct 13, 2015 at 14:04

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.

• Unicode 0x1d4a9 $\unicode{x1d4a9}$ Commented Oct 13, 2015 at 14:04

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.