homework3

minihomework3/PMM.ipynb

@@ -94,9 +94,9 @@
     "    \\sum_{k = 1}^{K} P(y_{j} | \\gamma_{jk} = 1; \\theta^{(i)}) P(\\gamma_{jk} = 1; \\theta^{(i)})\n",
     "    \\sum_{k = 1}^{K} P(y_{j} | \\gamma_{jk} = 1; \\theta^{(i)}) P(\\gamma_{jk} = 1; \\theta^{(i)})\n",
     "} \\\\\n",
     "} \\\\\n",
     "& = \\frac{\n",
     "& = \\frac{\n",
-    "    \\frac{\\alpha_{k} \\lambda_{k}^{y_{j}}}{y_{j} !} e^{- \\lambda_{k}}\n",
+    "    \\alpha_{k}^{(i)} \\frac{\\left( \\lambda_{k}^{(i)} \\right)^{y_{j}}}{y_{j} !} e^{- \\lambda_{k}^{(i)}}\n",
     "}{\n",
     "}{\n",
-    "    \\sum_{k = 1}^{K} \\frac{\\alpha_{k} \\lambda_{k}^{y_{j}}}{y_{j} !} e^{- \\lambda_{k}}\n",
+    "    \\sum_{k = 1}^{K} \\alpha_{k}^{(i)} \\frac{ \\left( \\lambda_{k}^{(i)} \\right)^{y_{j}}}{y_{j} !} e^{- \\lambda_{k}^{(i)}}\n",
     "} \\\\\n",
     "} \\\\\n",
     "\\end{aligned} \\tag {5}$$\n",
     "\\end{aligned} \\tag {5}$$\n",
     "\n",
     "\n",
@@ -136,9 +136,9 @@
     "\n",
     "\n",
     "$$\\begin{aligned}\n",
     "$$\\begin{aligned}\n",
     "\\hat{\\gamma}_{jk} = \\frac{\n",
     "\\hat{\\gamma}_{jk} = \\frac{\n",
-    "    \\frac{\\alpha_{k} \\lambda_{k}^{y_{j}}}{y_{j} !} e^{- \\lambda_{k}}\n",
+    "    \\alpha_{k}^{(i)} \\frac{\\left( \\lambda_{k}^{(i)} \\right)^{y_{j}}}{y_{j} !} e^{- \\lambda_{k}^{(i)}}\n",
     "}{\n",
     "}{\n",
-    "    \\sum_{k = 1}^{K} \\frac{\\alpha_{k} \\lambda_{k}^{y_{j}}}{y_{j} !} e^{- \\lambda_{k}}\n",
+    "    \\sum_{k = 1}^{K} \\alpha_{k}^{(i)} \\frac{ \\left( \\lambda_{k}^{(i)} \\right)^{y_{j}}}{y_{j} !} e^{- \\lambda_{k}^{(i)}}\n",
     "} \\\\\n",
     "} \\\\\n",
     "\\end{aligned}$$\n",
     "\\end{aligned}$$\n",
     "\n",
     "\n",