fixed missing dependencies in Conditional_Expectation_Gaussian.ipynb

Author: unpingco

Conditional_Expectation_Gaussian.ipynb

@@ -1,6 +1,6 @@
 {
  "metadata": {
-  "name": "Conditional_Expectation_Gaussian"
+  "name": ""
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -99,7 +99,8 @@
      "collapsed": false,
      "input": [
       "from sympy import Matrix, Symbol, exp, pi, simplify, integrate \n",
-      "from sympy import stats\n",
+      "from sympy import stats, sqrt, oo, use\n",
+      "from sympy.abc import y,x\n",
       "\n",
       "sigma_x = Symbol('sigma_x',positive=True)\n",
       "sigma_y = Symbol('sigma_y',positive=True)\n",
@@ -115,7 +116,7 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 3
+     "prompt_number": 13
     },
     {
      "cell_type": "markdown",
@@ -139,21 +140,15 @@
      "metadata": {},
      "outputs": [
       {
-       "latex": [
-        "$$\\frac{\\sigma_{xy} y}{\\sigma_{y}^{2}}$$"
-       ],
+       "metadata": {},
        "output_type": "pyout",
-       "png": "iVBORw0KGgoAAAANSUhEUgAAABwAAAApCAYAAAAmukmKAAAABHNCSVQICAgIfAhkiAAAAipJREFU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\n",
-       "prompt_number": 7,
+       "prompt_number": 14,
        "text": [
-        "sigma_xy\u22c5y\n",
-        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
-        "        2 \n",
-        " sigma_y  "
+        "sigma_xy*y/sigma_y**2"
        ]
       }
      ],
-     "prompt_number": 7
+     "prompt_number": 14
     },
     {
      "cell_type": "markdown",