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nest-open-source / nest-learning-thermostat / 5.0 / boost / 317601cb979f96545d0e892ce7cfdf59f676ee0a / . / boost_1_45_0 / libs / math / doc / sf_and_dist / equations / hypergeometric6.mml
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<?xml version='1.0'?>
<!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN'
'http://www.w3.org/TR/MathML2/dtd/xhtml-math11-f.dtd'
[<!ENTITY mathml 'http://www.w3.org/1998/Math/MathML'>]>
<html xmlns='http://www.w3.org/1999/xhtml'>
<head><title>hypergeometric6</title>
<!-- MathML created with MathCast Equation Editor version 0.89 -->
</head>
<body>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mtable>
<mtr>
<mtd>
<mtext>mean</mtext>
<mspace width="1em"/>
<mo>=</mo>
<mspace width="1em"/>
<mfrac>
<mrow>
<mi>r</mi>
<mi>n</mi>
</mrow>
<mi>N</mi>
</mfrac>
</mtd>
</mtr>
<mtr>
<mtd>
<mtext>mode</mtext>
<mspace width="1em"/>
<mo>=</mo>
<mspace width="1em"/>
<mtext>floor</mtext>
<mfenced>
<mrow>
<mfrac>
<mrow>
<mfenced>
<mrow>
<mi>r</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</mfenced>
<mfenced>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</mfenced>
</mrow>
<mrow>
<mi>N</mi>
<mo>+</mo>
<mn>2</mn>
</mrow>
</mfrac>
</mrow>
</mfenced>
</mtd>
</mtr>
<mtr>
<mtd>
<mtext>variance</mtext>
<mspace width="1em"/>
<mo>=</mo>
<mspace width="1em"/>
<mfrac>
<mrow>
<mi>r</mi>
<mfenced>
<mrow>
<mfrac>
<mi>n</mi>
<mi>N</mi>
</mfrac>
</mrow>
</mfenced>
<mfenced>
<mrow>
<mn>1</mn>
<mo>&#x2212;</mo>
<mfrac>
<mi>n</mi>
<mi>N</mi>
</mfrac>
</mrow>
</mfenced>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mi>r</mi>
</mrow>
</mfenced>
</mrow>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mn>1</mn>
</mrow>
</mfenced>
</mfrac>
</mtd>
</mtr>
<mtr>
<mtd>
<mtext>skewness</mtext>
<mspace width="1em"/>
<mo>=</mo>
<mspace width="1em"/>
<mfrac>
<mrow>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mn>2</mn>
<mi>n</mi>
</mrow>
</mfenced>
<msqrt>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mn>1</mn>
</mrow>
</mfenced>
</msqrt>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mn>2</mn>
<mi>r</mi>
</mrow>
</mfenced>
</mrow>
<mrow>
<msqrt>
<mrow>
<mi>r</mi>
<mi>n</mi>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mi>n</mi>
</mrow>
</mfenced>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mi>r</mi>
</mrow>
</mfenced>
</mrow>
</msqrt>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mn>2</mn>
</mrow>
</mfenced>
</mrow>
</mfrac>
</mtd>
</mtr>
<mtr>
<mtd>
<mtext>kurtosis excess</mtext>
<mspace width="1em"/>
<mo>=</mo>
<mspace width="1em"/>
<mfenced>
<mrow>
<mfrac>
<mrow>
<msup>
<mi>N</mi>
<mn>2</mn>
</msup>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mn>1</mn>
</mrow>
</mfenced>
</mrow>
<mrow>
<mi>r</mi>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mn>2</mn>
</mrow>
</mfenced>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mn>3</mn>
</mrow>
</mfenced>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mi>r</mi>
</mrow>
</mfenced>
</mrow>
</mfrac>
</mrow>
</mfenced>
<mfenced>
<mrow>
<mfrac>
<mrow>
<mi>N</mi>
<mfenced>
<mrow>
<mi>N</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</mfenced>
<mo>&#x2212;</mo>
<mn>6</mn>
<mi>N</mi>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mi>r</mi>
</mrow>
</mfenced>
</mrow>
<mrow>
<mi>n</mi>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mi>n</mi>
</mrow>
</mfenced>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>3</mn>
<mi>r</mi>
<mfenced>
<mrow>
<mi>N</mi>
<mo>&#x2212;</mo>
<mi>r</mi>
</mrow>
</mfenced>
<mfenced>
<mrow>
<mi>N</mi>
<mo>+</mo>
<mn>6</mn>
</mrow>
</mfenced>
</mrow>
<mrow>
<msup>
<mi>N</mi>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>&#x2212;</mo>
<mn>6</mn>
</mrow>
</mfenced>
</mtd>
</mtr>
</mtable>
</mrow>
</math>
</body>
</html>