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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Independence<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 />
Two events A <strong>and</strong> B are <strong>in</strong>dependent if P(A ∩B) = P(A)P(B).<br />
Two r<strong>and</strong>om variables X <strong>and</strong> Y are <strong>in</strong>dependent if for any two<br />
sets <strong>of</strong> possible outcomes A <strong>and</strong> B,<br />
P (X ∈ A,Y ∈ B) = P (X ∈ A)P (Y ∈ B).<br />
If X <strong>and</strong> Y are <strong>in</strong>dependent, then cov(X,Y ) = 0.<br />
However, cov(X,Y ) = 0 does not, <strong>in</strong> general, imply<br />
<strong>in</strong>dependence!
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