Finish lecture 10 notes

lectures/lecture10/lecturenotes.tex

@@ -27,7 +27,6 @@
         of the statistics; eg. sample mean
     \2 \textit{When might your samples not be independent of each other?}
         \3 This is key because a lot of statistical tests require iid variables
-    \2 Sampling w/ replacement vs. w/o replacement: relationship to independance
     \2 You can multiply together probs. when independent, have to start using
         conditional probabilities when not
     \2 \textit{Why do we consider our measurements random variables?}
@@ -35,6 +34,14 @@
     \2 \textit{How do we calculate probability a value will be within a range?}
         \3 Integral (CDF) at point $b$, minus integral at point $a$
 
+\1 Some probability basics
+    \2 ``trials''
+    \2 Probability must be in range 0 to 1
+    \2 Independence
+    \2 Adding: mostly used for mutually exclusive events in the same trial
+    \2 Multiplication: Used to calculate probability across multiple trials
+    \2 Sampling w/ replacement vs. w/o replacement: relationship to independence
+
 \1 Important probability concept: Expectation 
     \2 ``The value you can expect to get''
     \2 AKA the mean
@@ -75,7 +82,13 @@
     \2 Can only multiply means if independent
     \2 \textit{When to use arithmetic vs. Geometric vs. harmonic mean}
 
-\1 TODO: Means of ratios
+\1 Means of ratios
+    \2 Case 1: Sum of numerators and denominators both have physical meanings
+        \3 eg. sum of CPU busy times over sum of experiment durations
+    \2 Case 1a: Arithmetic mean can be used if bases are constant
+    \2 Case 1b: Harmonic mean can be used if numerators are constant
+    \2 Case 2: If cases are ``expected'' to be $a_i = cb_i$, can estimate
+        $c$ by taking geometric mean
 
 \1 Picking index of dispersion
     \2 Range (when bounded)