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<ml:apply> <ml:id xml:space="preserve">p1</ml:id> <ml:real>0.5</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.816227766016838</ml:real> </result> </ml:eval> </math> <rendering item-idref="20"/> </region> <region region-id="195" left="330" top="393" width="71.25" height="12.75" align-x="363.75" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve">p2</ml:id> <ml:real font="0">0.5</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.18377223398316206</ml:real> </result> </ml:eval> </math> <rendering item-idref="21"/> </region> <region region-id="202" left="192" top="422.25" width="319.5" height="48" align-x="192" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204"> <inlineAttr line-through="false">Практически формулами (3) ввиду их приближенности можно пользоваться только при "np , n(1-p)" больших 10.</inlineAttr> </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204"> <inlineAttr line-through="false">Рассмотрим функцию, которая точно задает границы изображенной на рис.1 области, если положить f(z,p) нулю.</inlineAttr> </f> </p> </text> </region> <region region-id="204" left="234" top="482.25" width="132" height="33.75" align-x="264" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">f</ml:id> <ml:boundVars> <ml:id xml:space="preserve">p</ml:id> <ml:id xml:space="preserve">z</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">z</ml:id> <ml:id xml:space="preserve">p</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">x</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:id xml:space="preserve">p</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">p</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="22"/> </region> <region region-id="208" left="432" top="495" width="12.75" height="12.75" align-x="437.25" align-y="504" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>4</ml:real> </ml:parens> </math> <rendering item-idref="23"/> </region> <region region-id="209" left="228" top="518.25" width="74.25" height="12" align-x="228" align-y="528" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204"> <inlineAttr line-through="false">Откуда следует:</inlineAttr> </f> </p> </text> </region> <region region-id="206" left="174" top="524.25" width="28.5" height="12" align-x="174" align-y="534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204"> <inlineAttr line-through="false">Рис. 1</inlineAttr> </f> </p> </text> </region> <region region-id="212" left="216" top="536.25" width="113.25" height="29.25" align-x="243" align-y="552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">z1</ml:id> <ml:boundVars> <ml:id xml:space="preserve">p</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">p</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">p</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">p</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="213" left="348" top="536.25" width="112.5" height="29.25" align-x="375" align-y="552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">z2</ml:id> <ml:boundVars> <ml:id xml:space="preserve">p</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">p</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">x</ml:id> <ml:apply> <ml:sqrt/> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:sqrt/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">p</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">p</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="214" left="480" top="543" width="12.75" height="12.75" align-x="485.25" align-y="552" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:parens xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:real>5</ml:real> </ml:parens> </math> <rendering item-idref="26"/> </region> <region region-id="218" left="6" top="584.25" width="474" height="48" align-x="6" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204"> <inlineAttr line-through="false">Очевидно, что для формул (5) специальный график строить не надо. Он уже есть на рис. 1. Надо только по оси ординат откладывать z1, z2, а по оси абсцисс - " p".</inlineAttr> </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204"> <inlineAttr line-through="false">С другой стороны, по формуле (4) можно построить поверхность уровней, в т.ч. содержащую нулевой уровень (см. рис. 2). Для этого</inlineAttr> </f> </p> </text> </region> <region region-id="219" left="6" top="645" width="22.5" height="12.75" align-x="16.5" align-y="654" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">a</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="220" left="48" top="645" width="37.5" height="12.75" align-x="57" align-y="654" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:real>0</ml:real> <ml:real>14</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="223" left="96" top="645" width="39" height="12.75" align-x="106.5" align-y="654" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:real>0</ml:real> <ml:real>10</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="222" left="156" top="638.25" width="87.75" height="27.75" align-x="183" align-y="654" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">M</ml:id> <ml:sequence> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:apply> <ml:div/> <ml:id xml:space="preserve">k</ml:id> <ml:real>10</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">j</ml:id> <ml:id xml:space="preserve">a</ml:id> </ml:apply> <ml:real>10</ml:real> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="229" left="30" top="750" width="181.5" height="204" align-x="120" align-y="750" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <component hide-arguments="false" clsid-buddy="62e334b8-fdda-4b2b-9bb4-48def95f2af1" item-idref="31" disable-calc="false"> <inputs> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">M</ml:id> </inputs> <outputs/> </component> <rendering item-idref="32"/> </region> <region region-id="234" left="162" top="848.25" width="28.5" height="12" align-x="162" align-y="858" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204"> <inlineAttr line-through="false">Рис. 2</inlineAttr> </f> </p> </text> </region> <region region-id="168" left="48" top="924.75" width="387.75" height="27" align-x="48" align-y="936" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr line-through="false">Пример построения трехмерного графика поверхности эллиптического</inlineAttr> </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr line-through="false">параболоида (</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="10"> <inlineAttr line-through="false">см. Выгодский, стр.213</inlineAttr> </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr line-through="false">)</inlineAttr> </f> </p> </text> </region> <region region-id="127" left="48" top="956.25" width="69.75" height="33.75" align-x="78.75" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve">g</ml:id> <ml:boundVars> <ml:id xml:space="preserve">r</ml:id> <ml:id xml:space="preserve">s</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">r</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">s</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="33"/> </region> <region region-id="143" left="144" top="969" width="33" height="12.75" align-x="160.5" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">R1</ml:id> <ml:real>20</ml:real> </ml:define> </math> <rendering item-idref="34"/> </region> <region region-id="144" left="198" top="969" width="32.25" height="12.75" align-x="213.75" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">S1</ml:id> <ml:real>40</ml:real> </ml:define> </math> <rendering item-idref="35"/> </region> <region region-id="145" left="258" top="969" width="43.5" height="12.75" align-x="271.5" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">r1</ml:id> <ml:range> <ml:real>0</ml:real> <ml:id xml:space="preserve">R1</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="36"/> </region> <region region-id="146" left="324" top="969" width="44.25" height="12.75" align-x="339" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">s1</ml:id> <ml:range> <ml:real>0</ml:real> <ml:id xml:space="preserve">S1</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="172" left="6" top="990.75" width="483" height="25.5" align-x="6" align-y="1002" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204"> <inlineAttr line-through="false">Здесь: </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false">"r"</inlineAttr> </f> <f family="Arial Cyr" charset="204"> <inlineAttr line-through="false"> изменяется от -1 до 1;<sp count="3"/> </inlineAttr> </f> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false">"s"</inlineAttr> </f> <f family="Arial Cyr" charset="204"> <inlineAttr line-through="false"> <sp/> </inlineAttr> </f> <f family="Arial Cyr" charset="204">изменяется от -2 до 2. Эти переменные переводятся в дискретное представление. В дискретных точках определяется "g(r,s)" , значения которой записываются в матрицу Q.</f> </p> </text> </region> <region region-id="149" left="48" top="1031.25" width="133.5" height="42.75" align-x="81" align-y="1062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:sequence> <ml:id xml:space="preserve">r1</ml:id> <ml:id xml:space="preserve">s1</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:id xml:space="preserve">g</ml:id> <ml:sequence> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">r1</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">R1</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>10</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">s1</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve">S1</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:real>10</ml:real> </ml:apply> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="38"/> </region> <region region-id="161" left="192" top="1053" width="51.75" height="18" align-x="226.5" align-y="1062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:sequence> <ml:real>20</ml:real> <ml:real>20</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="39"/> </region> <region region-id="162" left="246" top="1053" width="47.25" height="18" align-x="276" align-y="1062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:sequence> <ml:real>0</ml:real> <ml:real>20</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="163" left="300" top="1053" width="51.75" height="18" align-x="334.5" align-y="1062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:sequence> <ml:real>10</ml:real> <ml:real>40</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="41"/> </region> <region region-id="164" left="354" top="1053" width="47.25" height="18" align-x="384" align-y="1062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">Q</ml:id> <ml:sequence> <ml:real>10</ml:real> <ml:real>0</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="42"/> </region> <region region-id="147" left="36" top="1104" width="181.5" height="204" align-x="126" align-y="1104" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <component hide-arguments="false" clsid-buddy="62e334b8-fdda-4b2b-9bb4-48def95f2af1" item-idref="43" disable-calc="false"> <inputs> <ml:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Q</ml:id> </inputs> <outputs/> </component> <rendering item-idref="44"/> </region> <region region-id="183" left="198" top="1122.75" width="235.5" height="103.5" align-x="198" align-y="1134" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr line-through="false">ВНИМАНИЕ! Масштаб по осям д. б. одинаковым. Тогда картинка становится правдоподобной!</inlineAttr> </f> </p> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"> <f family="Arial Cyr" charset="204"> <inlineAttr line-through="false">Первый индекс Q -"r1" номер строки - соответствует оси абсцисс, второй индекс - "s1" номер столбца - соответствует оси ординат. Это всегда так?! 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