Differences

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--- users:pavelda2:sandbox [2015/05/30 22:15] – vytvořeno pavelda2
+++ users:pavelda2:sandbox [2015/05/30 22:48] (current) – [MI-SPI] pavelda2
@@ Line 1: / Line 1: @@
+====== Sandbox ======
+===== MI-SPI =====
+^ <math>X_1</math>      ^ 1       ^ 2 ^
+| <math>P(X_1 = x_1)</math>   |    <math>\frac{1}{2}</math>     |    <math>\frac{1}{2}</math>     |
+<math>P=\left(
+\begin{matrix}
+& 1 \\
+  \frac{1}{2} & \frac{1}{2} \\
+ \end{matrix}
+\right) \Rightarrow X_1*P=X_2  </math>
+^ <math>X_2</math>      ^ 1       ^ 2 ^
+| <math>P(X_2 = x_2)</math>   |    <math>\frac{1}{4}</math>     |    <math>\frac{3}{4}</math>     |
+^ <math>X_1 / X_2 </math>      ^ 1       ^ 2 ^
+| <math>1</math>   |    <math>\frac{1}{8}</math>     |    <math>\frac{3}{8}</math>     |
+| <math>2</math>   |    <math>\frac{1}{8}</math>     |    <math>\frac{3}{8}</math>     |
+<math>H(X_1|X_2) = - \sum_{\forall x_1} \sum_{\forall x_2}
+  P(X_1=x_1,X_2=x_2) \cdot  log_{b}{
+    \frac{P(X_1=x_1,X_2=x_2)}{P(X_2=x_2)}
+  }
+  \quad = \quad -2 \cdot \frac{1}{8} \cdot \log_{2}{\frac{\frac 1 8}{\frac 1 4}} -2 \cdot  \frac{3}{8} \cdot \log_{2}{\frac{\frac 3 8}{\frac 3 4}}
+  \quad = \quad - \frac{1}{4} \cdot (-1) - \frac{3}{4} \cdot (-1) = 1
+</math>