diff --git a/content/Week_1_7/WS_1_7_solution.ipynb b/content/Week_1_7/WS_1_7_solution.ipynb index 1541bf9362c541555004e0d92208e9d9cd1f4aeb..2e4eb5bf87c64534e748b99f2ba4c7efb74fa884 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",