Commit 9a54cb61 authored by Robert Ricci's avatar Robert Ricci

Finish lecture 10 notes

parent c6d9b03e
......@@ -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)
......
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