From 65b401105344c5829861898c1f9740665a9f82e1 Mon Sep 17 00:00:00 2001
From: Tom van Woudenberg <t.r.vanwoudenberg@tudelft.nl>
Date: Wed, 16 Oct 2024 09:28:52 +0200
Subject: [PATCH] Nicer equations
---
content/Week_1_7/WS_1_7_solution.ipynb | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/content/Week_1_7/WS_1_7_solution.ipynb b/content/Week_1_7/WS_1_7_solution.ipynb
index 1541bf93..2e4eb5bf 100644
--- a/content/Week_1_7/WS_1_7_solution.ipynb
+++ b/content/Week_1_7/WS_1_7_solution.ipynb
@@ -294,7 +294,7 @@
" Fitting by moments a distribution implies equating the moments of the observations to those of the parametric distribution. Applying then the expressions of the mean and variance of the Gumbel distribution we obtain:\n",
" \n",
"$\n",
- " \\mathbb{V}ar(X) = \\frac{\\pi^2}{6} \\beta^2 \\to \\beta = \\sqrt{\\frac{6\\mathbb{V}ar(X)}{\\pi^2}}=\\sqrt{\\frac{6 \\cdot 16.797^2}{\\pi^2}}= 13.097\n",
+ " \\mathbb{V}ar(X) = \\cfrac{\\pi^2}{6} \\beta^2 \\to \\beta = \\sqrt{\\cfrac{6\\mathbb{V}ar(X)}{\\pi^2}}=\\sqrt{\\cfrac{6 \\cdot 16.797^2}{\\pi^2}}= 13.097\n",
"$\n",
"\n",
"$\n",
@@ -360,7 +360,7 @@
"Note: you can compute the values of the random variable using the inverse of the CDF of the Gumbel distribution:\n",
" \n",
"$\n",
- "F(x) = e^{-e^{-\\frac{x-\\mu}{\\beta}}} \\to x = -\\beta ln\\left(-lnF(x)\\right) + \\mu\n",
+ "F(x) = e^{\\normalsize -e^{\\normalsize-\\cfrac{x-\\mu}{\\beta}}} \\to x = -\\beta \\ln\\left(-\\ln F\\left(x\\right)\\right) + \\mu\n",
"$\n",
"\n",
"Compare and assess:\n",
--
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