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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Expected values, variance, <strong>and</strong> covariance<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 />
For a r<strong>and</strong>om variable X with a density f , the expected value<br />
<strong>of</strong> X is E(X) = ∫ ∞<br />
−∞<br />
xf (x)dx.<br />
The variance <strong>of</strong> X is V (X) = E([X − E(X)] 2 ).<br />
The covariance <strong>of</strong> two r<strong>and</strong>om variable X <strong>and</strong> Y is<br />
cov(X,Y ) = E [(X − E(X))(Y − E(Y ))].<br />
Two r<strong>and</strong>om variables with the same distribution functions are<br />
identically distributed.
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