add prml

yaoshengzhe · May 7, 2014 · 85b6701 · 85b6701
1 parent 4210931
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diff --git a/prml/01_introduction.md b/prml/01_introduction.md
@@ -66,3 +66,19 @@ p(g|orange) &= \frac{p(g, orange)}{p(orange)} \\
             &= 0.5
 \end{align*}
 
+### 1.5
+\begin{align*}
+var[f] &= E[(f(x) - E[f(x)])^2] \\
+       &= E[f(x)^2 - 2f(x)E[f(x)] + E^2[f(x)]] \\
+       &= E[f(x)^2] - E^2(f(x))
+\end{align*}
+
+### 1.6
+If $x$ and $y$ are independent, then $p(x, y) = p(x) \cdot p(y)$ and thus $E(x,y)=E(x)E(y)$.
+
+Therefore,
+\begin{align*}
+cov(x, y) &= E_{x,y}[(x-E[x])(y-E[y])] \\
+          &= E_{x,y}[xy] - E[x]E[y] \\
+          &= 0
+\end{align*}
diff --git a/prml/compile b/prml/compile
@@ -0,0 +1,3 @@
+#! /bin/bash
+
+pandoc `find . -name *$1*` -o test.pdf
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		@@ -0,0 +1,3 @@
		#! /bin/bash

		pandoc `find . -name $1` -o test.pdf