mathmlben
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Visualization for goldstandard
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text/mathml
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="upper R Subscript j Baseline equals StartFraction left-parenthesis n minus j right-parenthesis left-parenthesis j plus n plus gamma plus delta right-parenthesis left-parenthesis j plus gamma right-parenthesis left-parenthesis j plus delta right-parenthesis Over left-parenthesis gamma plus delta plus 2 j right-parenthesis left-parenthesis gamma plus delta plus 2 j plus 1 right-parenthesis EndFraction">
<semantics>
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<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="0" data-semantic-parent="2">R</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="1" data-semantic-parent="2">j</mi>
</mrow>
</msub>
<mo data-semantic-type="relation" data-semantic-role="equality" data-semantic-id="3" data-semantic-parent="69" data-semantic-operator="relseq,=">=</mo>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="4" data-semantic-parent="29" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="subtraction" data-semantic-id="28" data-semantic-children="5,7" data-semantic-content="6" data-semantic-parent="29">
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<mo data-semantic-type="operator" data-semantic-role="subtraction" data-semantic-id="6" data-semantic-parent="28" data-semantic-operator="infixop,−">−
<!-- − -->
</mo>
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="7" data-semantic-parent="28">j</mi>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="8" data-semantic-parent="29" data-semantic-operator="fenced">)</mo>
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="36" data-semantic-parent="39" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="31" data-semantic-children="30" data-semantic-content="9,17" data-semantic-parent="39">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="9" data-semantic-parent="31" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="30" data-semantic-children="10,12,14,16" data-semantic-content="11,13,15" data-semantic-parent="31">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="10" data-semantic-parent="30">j</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="11" data-semantic-parent="30" data-semantic-operator="infixop,+">+</mo>
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="12" data-semantic-parent="30">n</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="13" data-semantic-parent="30" data-semantic-operator="infixop,+">+</mo>
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="14" data-semantic-parent="30">γ
<!-- γ -->
</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="15" data-semantic-parent="30" data-semantic-operator="infixop,+">+</mo>
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="16" data-semantic-parent="30">δ
<!-- δ -->
</mi>
</mrow>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="17" data-semantic-parent="31" data-semantic-operator="fenced">)</mo>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="37" data-semantic-parent="39" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="33" data-semantic-children="32" data-semantic-content="18,22" data-semantic-parent="39">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="18" data-semantic-parent="33" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="32" data-semantic-children="19,21" data-semantic-content="20" data-semantic-parent="33">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="19" data-semantic-parent="32">j</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="20" data-semantic-parent="32" data-semantic-operator="infixop,+">+</mo>
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="21" data-semantic-parent="32">γ
<!-- γ -->
</mi>
</mrow>
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="22" data-semantic-parent="33" data-semantic-operator="fenced">)</mo>
</mrow>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="38" data-semantic-parent="39" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="35" data-semantic-children="34" data-semantic-content="23,27" data-semantic-parent="39">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="23" data-semantic-parent="35" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="34" data-semantic-children="24,26" data-semantic-content="25" data-semantic-parent="35">
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="24" data-semantic-parent="34">j</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="25" data-semantic-parent="34" data-semantic-operator="infixop,+">+</mo>
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="26" data-semantic-parent="34">δ
<!-- δ -->
</mi>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="27" data-semantic-parent="35" data-semantic-operator="fenced">)</mo>
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</mrow>
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<mrow data-semantic-type="fenced" data-semantic-role="leftright" data-semantic-id="61" data-semantic-children="58" data-semantic-content="40,47" data-semantic-parent="67">
<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="40" data-semantic-parent="61" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="58" data-semantic-children="41,43,60" data-semantic-content="42,44" data-semantic-parent="61">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="41" data-semantic-parent="58">γ
<!-- γ -->
</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="42" data-semantic-parent="58" data-semantic-operator="infixop,+">+</mo>
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="43" data-semantic-parent="58">δ
<!-- δ -->
</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="44" data-semantic-parent="58" data-semantic-operator="infixop,+">+</mo>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="60" data-semantic-children="45,46" data-semantic-content="59" data-semantic-parent="58">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="45" data-semantic-parent="60">2</mn>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="59" data-semantic-parent="60" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="46" data-semantic-parent="60">j</mi>
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<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="66" data-semantic-parent="67" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="open" data-semantic-id="48" data-semantic-parent="65" data-semantic-operator="fenced">(</mo>
<mrow data-semantic-type="infixop" data-semantic-role="addition" data-semantic-id="62" data-semantic-children="49,51,64,56" data-semantic-content="50,52,55" data-semantic-parent="65">
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="49" data-semantic-parent="62">γ
<!-- γ -->
</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="50" data-semantic-parent="62" data-semantic-operator="infixop,+">+</mo>
<mi data-semantic-type="identifier" data-semantic-role="greekletter" data-semantic-font="italic" data-semantic-id="51" data-semantic-parent="62">δ
<!-- δ -->
</mi>
<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="52" data-semantic-parent="62" data-semantic-operator="infixop,+">+</mo>
<mrow data-semantic-type="infixop" data-semantic-role="implicit" data-semantic-id="64" data-semantic-children="53,54" data-semantic-content="63" data-semantic-parent="62">
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="53" data-semantic-parent="64">2</mn>
<mo data-semantic-type="operator" data-semantic-role="multiplication" data-semantic-id="63" data-semantic-parent="64" data-semantic-added="true" data-semantic-operator="infixop,"></mo>
<mi data-semantic-type="identifier" data-semantic-role="latinletter" data-semantic-font="italic" data-semantic-id="54" data-semantic-parent="64">j</mi>
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<mo data-semantic-type="operator" data-semantic-role="addition" data-semantic-id="55" data-semantic-parent="62" data-semantic-operator="infixop,+">+</mo>
<mn data-semantic-type="number" data-semantic-role="integer" data-semantic-font="normal" data-semantic-id="56" data-semantic-parent="62">1</mn>
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<mo stretchy="false" data-semantic-type="fence" data-semantic-role="close" data-semantic-id="57" data-semantic-parent="65" data-semantic-operator="fenced">)</mo>
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</mfrac>
</mrow>
</mrow>
<annotation encoding="application/x-tex">R_{j}={\frac {(n-j)(j+n+\gamma +\delta )(j+\gamma )(j+\delta )}{(\gamma +\delta +2j)(\gamma +\delta +2j+1)}}</annotation>
</semantics>
</math>