From e8b88adf5f83a4a75d9dd72ba99af8410e54706e Mon Sep 17 00:00:00 2001 From: Roger Labbe Date: Mon, 29 Jan 2018 09:27:24 -0800 Subject: [PATCH] GitHub #154 Description of VAR inconsistent I stated that the heights are equally probable, which they are not. --- 03-Gaussians.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/03-Gaussians.ipynb b/03-Gaussians.ipynb index 3f42551..c239656 100644 --- a/03-Gaussians.ipynb +++ b/03-Gaussians.ipynb @@ -513,7 +513,7 @@ "\n", "$$\\mathit{VAR}(X) = E[(X - \\mu)^2]$$\n", "\n", - "Ignoring the squaring for a moment, you can see that the variance is the *expected value* for how much the sample space $X$ varies from the mean $\\mu:$ ($X-\\mu)$. I will explain the purpose of the squared term later. We have the formula for the expected value $E[X] = \\sum\\limits_{i=1}^n p_ix_i$, and we will assume that any height is equally probable, so we can substitute that into the equation above to get\n", + "Ignoring the squaring for a moment, you can see that the variance is the *expected value* for how much the sample space $X$ varies from the mean $\\mu:$ ($X-\\mu)$. I will explain the purpose of the squared term later. We have the formula for the expected value $E[X] = \\sum\\limits_{i=1}^n p_ix_i$ so we can substitute that into the equation above to get\n", "\n", "$$\\mathit{VAR}(X) = \\frac{1}{n}\\sum_{i=1}^n (x_i - \\mu)^2$$\n", " \n",