added N(mu,sigma) notation

Gaussians.ipynb

@@ -100,7 +100,7 @@
      "source": [
       "You will not need to understand how this equation comes about, or remember it for this book, but it is useful to look at it to see how it works. Specifically, notice the term for $e$. When $x==\\mu$, the term reduces to $e^0=1$. Any other value of x will result in a smaller value for the exponent term due to the negative sign, so the curve will always be highest at $x==\\mu$.\n",
       "\n",
-      "Now we will plot a gaussian centered around 23 ($\\mu=23$), with a variance of 1 ($\\sigma^2=1$)."
+      "Now we will plot a gaussian centered around 23 ($\\mu=23$), with a variance of 1 ($\\sigma^2=1$). "
      ]
     },
     {
@@ -171,7 +171,9 @@
      "source": [
       "So what is this telling us? The blue gaussian is very narrow. It is saying that we believe x=23, and that we are very sure about that. In contrast, the red gaussian also believes that x=23, but we are much less sure about that. Our believe that x=23 is lower, and so our belief about the likely possible values for x is spread out - we think it is quite likely that x=2 or x=8, for example. The blue gaussian has almost completely eliminated 22 or 24 as possible value - their probably is almost 0.0, whereas the red curve considers them nearly as likely as 23.\n",
       "\n",
-      "If we think back to the thermometer, we can consider these three curves as representing 3 thermometers. The blue curve represents a very accurate thermometer, and the red one represents a fairly inaccurate one. Green of course represents one in between the two others. Note the very powerful property the Gaussian distribution affords us - we can entirely represent both the reading and the error of a thermometer with only two numbers - the mean and the variance.\n"
+      "If we think back to the thermometer, we can consider these three curves as representing 3 thermometers. The blue curve represents a very accurate thermometer, and the red one represents a fairly inaccurate one. Green of course represents one in between the two others. Note the very powerful property the Gaussian distribution affords us - we can entirely represent both the reading and the error of a thermometer with only two numbers - the mean and the variance.\n",
+      "\n",
+      "The standard notation for a normal distribution is just $N(\\mu,\\sigma^2)$. I will not go into detail as to why $\\sigma^2$ is used, other than to note that $\\sigma$ is commonly called the *standard deviation*, which has enormous utility in statistics. The standard deviation is not really used in this book, so I will not address it further. The important thing to understand is that the variance ($\\sigma^2$) is a measure of the width of the curve. The curve above is notated as $N(23, 1)$, since $\\mu=23$ and $\\sigma=1$. We will use this notiation throughout the rest of the book, so learn it now.\n"
      ]
     },
     {