Update lab_08_pi.ipynb

book/labs/4_rng/lab_08/lab_08_pi.ipynb

@@ -87,17 +87,19 @@
     "## <span style=\"color:orange;\"> A Monte Carlo Experiment </span>\n",
     "\n",
     "Recall that a uniform random variable $U$ on the interval $(0,1)$ has a probability density function defined as follows:\n",
+    "\n",
     "$$ f_U(u) = \\begin{cases}\n",
-    "    1 &, 0<u<1 \\\\\n",
-    "    0 &, \\text{ otherwise}\n",
+    "    1 , &0<u<1 \\\\\n",
+    "    0 , &\\text{ otherwise}\n",
     "\\end{cases} $$\n",
     "\n",
     "So the probability $U$ takes a value in a subinterval $(s,t)$ of $(0,1)$ is exactly the length $t-s$ of the subinterval.\n",
     "\n",
     "More genrerally, a uniform random variable $V$ on the interval $(a,b)$ has probability density function \n",
+    "\n",
     "$$ f_V(v) = \\begin{cases}\n",
-    "    \\frac{1}{b-a} &, a<v<b \\\\\n",
-    "    0 &, \\text{ otherwise}\n",
+    "    \\frac{1}{b-a}, &a<v<b \\\\\n",
+    "    0, &\\text{ otherwise}\n",
     "\\end{cases} $$"
    ]
   },