Elaborate a bit on adding a constant to a Gaussian r.v.

Author: liviu-

bayesian_linear_regression.ipynb

@@ -162,7 +162,7 @@
     "\n",
     "$$ y = \\mathbf{w}^T\\mathbf{g}(x) + \\epsilon $$\n",
     "\n",
-    "Therefore, combining the two terms we can say that $p(\\mathbf{y}|\\mathbf{x},\\mathbf{w}) \\sim \\mathcal{N}(\\mathbf{w}^T\\mathbf{g}(x), \\sigma^2)$.\n",
+    "Therefore, adding a constant to a Gaussian random variable results in a shift of the mean (from 0 to $\\mathbf{w}^T\\mathbf{g}(x)$), so we can say that $p(\\mathbf{y}|\\mathbf{x},\\mathbf{w}) \\sim \\mathcal{N}(\\mathbf{w}^T\\mathbf{g}(x), \\sigma^2)$.\n",
     "\n",
     "## Maximum Likelihood\n",
     "\n",