Fix typo in euqation 1

gaussian_processes.ipynb

@@ -20,7 +20,7 @@
     "\n",
     "Another example of non-parametric methods are [Gaussian processes](https://en.wikipedia.org/wiki/Gaussian_process) (GPs). Gaussian processes are regression models that can also estimate the uncertainty of predictions. They can also be used for classification e.g. in context of logistic regression. A Gaussian process is a random process where any point $\\mathbf{x} \\in \\mathbb{R}^d$ is assigned a random variable $f(\\mathbf{x})$ and where the joint distribution of a finite number of these variables $p(f(\\mathbf{x}_1),...,f(\\mathbf{x}_N))$ is itself Gaussian:\n",
     "\n",
-    "$$P(\\mathbf{f} \\lvert \\mathbf{X}) = \\mathcal{N}(\\mathbf{f} \\lvert \\boldsymbol\\mu, \\mathbf{K})\\tag{1}\\label{eq1}$$\n",
+    "$$p(\\mathbf{f} \\lvert \\mathbf{X}) = \\mathcal{N}(\\mathbf{f} \\lvert \\boldsymbol\\mu, \\mathbf{K})\\tag{1}\\label{eq1}$$\n",
     "\n",
     "In Equation $(1)$, $\\mathbf{f} = (f(\\mathbf{x}_1),...,f(\\mathbf{x}_N))$, $\\boldsymbol\\mu = (m(\\mathbf{x}_1),...,m(\\mathbf{x}_N))$ and $K_{ij} = \\kappa(\\mathbf{x}_i,\\mathbf{x}_j)$. $m$ is the mean function and it is common to use $m(\\mathbf{x}) = 0$ as GPs are flexible enough to model the mean arbitrarily well. $\\kappa$ is a positive definite *kernel function* or *covariance function*. Thus, a Gaussian process is a distribution over functions whose shape (smoothness, ...) is defined by $\\mathbf{K}$. If points $\\mathbf{x}_i$ and $\\mathbf{x}_j$ are considered to be similar by the kernel the function values at these points, $f(\\mathbf{x}_i)$ and $f(\\mathbf{x}_j)$, can be expected to be similar too.\n",
     "\n",