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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Laws <strong>of</strong> large numbers <strong>and</strong> the 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 strong law <strong>of</strong> large numbers, SLLN).<br />
Let X i ,i = 1, · · · ,n, be i.i.d r<strong>and</strong>om variables with<br />
E(X i ) = 0,V(X i ) = 1, <strong>and</strong> S n = ∑ n<br />
1 X i.<br />
Then with probability one,<br />
S n<br />
lim<br />
n→∞ n = 0.
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