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Robert Ricci
Evaluating Networked Systems
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9a54cb61
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Feb 11, 2014
by
Robert Ricci
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Finish lecture 10 notes
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lectures/lecture10/lecturenotes.tex
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@@ -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?
}
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@@ -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
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@@ -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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