AuditWiki

User Tools

Site Tools

Trace:
users:pavelda2:sandbox

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
users:pavelda2:sandbox [2015/05/30 22:43] – [MI-SPI] pavelda2users: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}
 +  0 & 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>
 +
 +