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EQ2EMu


			
				
					
						
						
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							<?xml version="1.0" encoding="UTF-8"?>
<!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 columnalign="right center left">
      <mtr>
        <mtd>
          <mtext>mean</mtext>
        </mtd>
        <mtd>
          <mo>=</mo>
        </mtd>
        <mtd>
          <mfrac>
            <mrow>
              <mi>r</mi>
              <mi>n</mi>
            </mrow>
            <mi>N</mi>
          </mfrac>
        </mtd>
      </mtr>
      <mtr>
        <mtd>
          <mtext>mode</mtext>
        </mtd>
        <mtd>
          <mo>=</mo>
        </mtd>
        <mtd>
          <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>
        </mtd>
        <mtd>
          <mo>=</mo>
        </mtd>
        <mtd>
          <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>
        </mtd>
        <mtd>
          <mo>=</mo>
        </mtd>
        <mtd>
          <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>
        </mtd>
        <mtd>
          <mo>=</mo>
        </mtd>
        <mtd>
          <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>