diff --git a/03-Gaussians.ipynb b/03-Gaussians.ipynb index fa6034e..b2e5db5 100644 --- a/03-Gaussians.ipynb +++ b/03-Gaussians.ipynb @@ -1408,8 +1408,8 @@ "$p(x) = \\int\\limits_{-\\infty}^\\infty f_2(x-x_1)f_1(x_1)\\, dx$\n", "\n", "$= \\int\\limits_{-\\infty}^\\infty \n", - "\\frac{1}{\\sqrt{2\\pi}\\sigma_z}\\exp\\left[-\\frac{x - z - \\mu_z}{2\\sigma^2_z}\\right]\n", - "\\frac{1}{\\sqrt{2\\pi}\\sigma_p}\\exp\\left[-\\frac{x - \\mu_p}{2\\sigma^2_p}\\right] \\, dx$\n", + "\\frac{1}{\\sqrt{2\\pi}\\sigma_z}\\exp\\left[-\\frac{(x - z - \\mu_z)^2}{2\\sigma^2_z}\\right]\n", + "\\frac{1}{\\sqrt{2\\pi}\\sigma_p}\\exp\\left[-\\frac{(x - \\mu_p)^2}{2\\sigma^2_p}\\right] \\, dx$\n", "\n", "$= \\int\\limits_{-\\infty}^\\infty\n", "\\frac{1}{\\sqrt{2\\pi}\\sqrt{\\sigma_p^2 + \\sigma_z^2}} \\exp\\left[ -\\frac{(x - (\\mu_p + \\mu_z)))^2}{2(\\sigma_z^2+\\sigma_p^2)}\\right]\n",