Overview of basic concepts in Statistics and Probability - SAMSI
Overview of basic concepts in Statistics and Probability - SAMSI
Overview of basic concepts in Statistics and Probability - SAMSI
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Sample spaces, cont<strong>in</strong>ued<br />
<strong>Overview</strong> <strong>of</strong><br />
<strong>basic</strong> <strong>concepts</strong><br />
<strong>in</strong> <strong>Statistics</strong><br />
<strong>and</strong><br />
<strong>Probability</strong><br />
Avanti<br />
Athreya<br />
Prelim<strong>in</strong>aries<br />
Important<br />
distributions,<br />
scal<strong>in</strong>g laws,<br />
<strong>and</strong> the CLT<br />
Parametric<br />
estimation <strong>and</strong><br />
hypothesis<br />
test<strong>in</strong>g<br />
A sample po<strong>in</strong>t ω ∈ Ω is a particular realization <strong>of</strong> the<br />
experiment <strong>and</strong> it cannot be determ<strong>in</strong>ed <strong>in</strong> advance <strong>of</strong><br />
perform<strong>in</strong>g the experiment.<br />
Example: ω =HHTH <strong>in</strong> the co<strong>in</strong> toss case.<br />
The sample space “encodes” all the r<strong>and</strong>omness <strong>in</strong> the sense<br />
that the specific realization <strong>of</strong> the experiment, i.e. ω ∈ Ω, is<br />
r<strong>and</strong>om.<br />
Once the specific realization is known (i.e. the experiment is<br />
performed), there is no more r<strong>and</strong>omness.
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