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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The Central Limit Theorem (CLT).<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 />
Theorem (The Central Limit Theorem, CLT).<br />
Let X i be i.i.d r<strong>and</strong>om variables with zero mean <strong>and</strong> unit<br />
variance.<br />
Then<br />
( )<br />
lim P Sn<br />
√ ≤ x = 1 ∫ x<br />
√ e − t2 2 dt<br />
n→∞ n 2π −∞<br />
The CLT accounts for the ubiquity <strong>of</strong> the Gaussian distribution.
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