<div id="Fd45d7188c" class='jxgbox' style="margin:auto;width: 350px; height: 350px;margin-top:20px;margin-bottom:15px;"></div> 
<script type="text/javascript"> 
var intex1_board2 = JXG.JSXGraph.initBoard('Fd45d7188c', {boundingbox: [110, 1.2, 200, -0.1], showcopyright: false, axes:true, shownavigation: false,grid:false,pan:{enabled:false}}); 
var absAxe = intex1_board2.create('arrow',[ [-5,-0.005],[200,-0.005] ], {strokeColor: 'black', strokeWidth:2,fixed:true}); 
var intex1_c1 = intex1_board2.create('functiongraph', [function (x) { return  Math.pow(2,(-0.01*((x-160)*(x-160)))); }]); 
var pinf2 = intex1_board2.create('point',[153,0],{name:'a'});
var psup2 = intex1_board2.create('point',[172,0],{name:'b'});
intex1_board2.on('move', function(){ 
    pinf2.moveTo([pinf2.X(),0]); 
    psup2.moveTo([psup2.X(),0]);
}); 
var intex1_i1 = intex1_board2.create('integral', [[function(){return pinf2.X()},function(){return psup2.X()} ], intex1_c1],{withLabel: false,fixed:true,fillColor:'blue'}); 
intex1_i1.curveLeft.setProperty({visible:false}); 
intex1_i1.curveRight.setProperty({visible:false});
for(var i=120;i<201;i=i+10){
  intex1_board2.create('segment',[ [i,-0.02] , [i,0.02] ],{strokeColor:'black',fixed:true});
  intex1_board2.create('text',[i-3,-0.05,i],{fixed:true});
}
</script>

<div id='box12Ax' class='jxgbox' style='width:350px; height:350px;margin:auto;margin-top:20px;margin-bottom:10px;'></div> 
<script type='text/javascript'> 
var brdre = JXG.JSXGraph.initBoard('box12Ax', {axis:true, boundingbox:[-5,0.2,140,-0.05], showCopyright:false,showNavigation:false,pan:{enabled:false}});
for(var k=0;k<200;k=k+50){
    brdre.create('text',[k-2,-0.015,k],{fixed:true});
    brdre.create('segment',[[k,-0.005],[k,0.005]],{fixed:true,strokeColor:'black'});
}
var n = brdre.create('slider',[[10,0.18],[80,0.18],[1,2,140]], {name:'n',snapWidth:1});
var prob = brdre.create('slider',[[10,0.15],[80,0.15],[0,.5,1]], {name:'p',snapWidth:0.01});
var sc = brdre.create('curve',[[0],[0]],{dash:0,strokeWidth:1,strokeColor:'red'});
sc.updateDataArray = function() {
   this.dataX = [];
   this.dataY = [];  
   for (var i=0;i<=n.Value();i++) {
     this.dataX.push(i);   
     this.dataY.push( binomial(n.Value(),i,prob.Value() ));   
     this.dataX.push(i);   
     this.dataY.push( 0 );    
   }  
}

function binomial(n, k, p) {
    var coeff = 1;
    for (var x = n - k + 1; x < n+1; x++) {
      coeff *= x;
    }
    for (x = 1; x < k+1; x++) {
      coeff /= x;
    }
    var p1=1;
    var p2=1;
    for (x=0; x < k; x++) {
       p1=p1*p;
    }
    for (x=0; x < n-k; x++) {
       p2=p2*(1-p);
    }
    return coeff*p1*p2;
}
</script>

<div id="d4boxF" class='jxgbox' style="margin:auto;width: 350px; height: 350px;margin-top:20px;margin-bottom:15px;"></div> 
<script type="text/javascript"> 
var intex1_board00 = JXG.JSXGraph.initBoard('d4boxF', {boundingbox: [-4, 0.5, 4, -0.05], showcopyright: false, axes:true, shownavigation: false,grid:false,pan:{enabled:false}}); 
var absAxe = intex1_board00.create('arrow',[ [-5,0.00],[4,0.00] ], {strokeColor: 'black', strokeWidth:2,fixed:true}); 
var absOrd = intex1_board00.create('arrow',[ [0,-1],[0,0.5] ], {strokeColor: 'black',fixed:true}); 
var intex1_c1 = intex1_board00.create('functiongraph', [function (x) { return  0.3989422804*Math.pow( 2.718281828,(-0.5*x*x) ); }]); 
var pinfA = intex1_board00.create('point',[-1.2,0],{name:'a'});
var psupA = intex1_board00.create('point',[1,0],{name:'b'});
intex1_board00.on('move', function(){ 
    pinfA.moveTo([pinfA.X(),0]); 
    psupA.moveTo([psupA.X(),0]);
}); 
var intex1_i1A = intex1_board00.create('integral', [[function(){return pinfA.X()},function(){return psupA.X()} ], intex1_c1],{withLabel: false,fixed:true,fillColor:'blue'}); 
intex1_i1A.curveLeft.setProperty({visible:false}); 
intex1_i1A.curveRight.setProperty({visible:false});
for(var i=-4;i<4;i=i+0.5){
  intex1_board00.create('segment',[ [i,-0.01] , [i,0.01] ],{strokeColor:'black',fixed:true,strokeWidth:1});
  intex1_board00.create('text',[i-0.2,-0.02,i],{fixed:true});
}
var t1 = intex1_board00.create('text',[function(){return (pinfA.X()+psupA.X())/2-0.5;},0.2,'
P(a< X < b)
'],{fixed:true});
var t2 = intex1_board00.create('text',[-3.5,0.45,function(){return 'P( a < X < b ) = '+intex1_i1A.Value(); }],{strokeColor:'blue'});
</script>

<div id="c12boxFs" class='jxgbox' style="margin:auto;width: 350px; height: 350px;margin-top:20px;margin-bottom:15px;"></div> 
<script type="text/javascript"> 
var boardGo = JXG.JSXGraph.initBoard('c12boxFs', {boundingbox: [-4.5, 0.5, 4.5, -0.05], showcopyright: false, axes:true, shownavigation: false,grid:false,pan:{enabled:false}}); 
var absAxe = boardGo.create('arrow',[ [-5,0.00],[4.5,0.00] ], {strokeColor: 'black', strokeWidth:2,fixed:true}); 
var absOrd = boardGo.create('arrow',[ [0,-1],[0,0.5] ], {strokeColor: 'black',fixed:true}); 
var c1 = boardGo.create('functiongraph', [function (x) { return  0.3989422804*Math.pow( 2.718281828,(-0.5*x*x) ); }]); 
var tmobileA = boardGo.create('slider',[[-2,0.45],[2,0.45],[0,1,5]],{name:'t',snapWidth:0.01});
var i1 = boardGo.create('integral', [[function(){return -tmobileA.Value();}, function(){return tmobileA.Value();} ] , c1],{withLabel: false,fixed:true,fillColor:'blue',label:{strokeColor:'blue',offset: [-60, -40],fontSize:10,fixed:true} }); 
i1.curveLeft.setProperty({visible:false}); 
i1.curveRight.setProperty({visible:false});
var i2 = boardGo.create('integral', [[-4.2, function(){return -tmobileA.Value();} ] , c1],{withLabel: false,fixed:true,fillColor:'green',label:{strokeColor:'green',offset: [-50, 10],fontSize:10} }); 
i2.curveLeft.setProperty({visible:false}); 
i2.curveRight.setProperty({visible:false});
var i3 = boardGo.create('integral', [[ function(){return tmobileA.Value();},4.2 ] , c1],{withLabel: false,fixed:true,fillColor:'green',label:{strokeColor:'green',offset: [-80, -80],fontSize:10} }); 
i3.curveLeft.setProperty({visible:false}); 
i3.curveRight.setProperty({visible:false});
boardGo.create('text',[-4,0.3,function(){var p = Math.floor(1000000*i1.Value())/1000000;var r = Math.round((-(p-1)/2)*1000000)/1000000;return '
1-2P( X > t ) = 1-2x'+Math.round(100000*r)/100000+' = '+Math.round(100000*p)/100000+'
';}],{fixed:true,strokeColor:'green'});
boardGo.create('text',[-4,0.35,function(){var p = Math.floor( i1.Value()*1000000 )/1000000;return '
P( -t < X < t )='+Math.round(100000*p)/100000+'
';}],{fixed:true,strokeColor:'blue'});
boardGo.create('text',[-4,0.25,function(){var p = Math.floor( i1.Value()*1000000 )/1000000;return '
P( X > t )= P( X < -t ) ='+Math.round((-(p-1)/2)*1000000)/1000000+'
';}],{fixed:true,strokeColor:'black'});
for(var i=-4;i<4;i=i+0.5){
  boardGo.create('segment',[ [i,-0.01] , [i,0.01] ],{strokeColor:'black',fixed:true,strokeWidth:1});
  boardGo.create('text',[i-0.2,-0.02,i],{fixed:true});
}
</script>

<div id="d4boxFt" class='jxgbox' style="margin:auto;width: 350px; height: 350px;margin-top:20px;margin-bottom:15px;"></div> 
<script type="text/javascript"> 
var intex1_board5 = JXG.JSXGraph.initBoard('d4boxFt', {boundingbox: [-4, 0.5, 4, -0.05], showcopyright: false, axes:true, shownavigation: false,grid:false,pan:{enabled:false}}); 
var absAxe = intex1_board5.create('arrow',[ [-5,0.00],[4,0.00] ], {strokeColor: 'black', strokeWidth:2,fixed:true}); 
var absOrd = intex1_board5.create('arrow',[ [0,-1],[0,0.5] ], {strokeColor: 'black',fixed:true}); 
var intex1_c1 = intex1_board5.create('functiongraph', [function (x) { return  0.3989422804*Math.pow( 2.718281828,(-0.5*x*x) ); }]); 
var pinfC = intex1_board5.create('slider',[[-3,0.47],[2,0.47],[-4,-1,5]],{name:'a',snapWidth:0.1});
var psupC = intex1_board5.create('slider',[[-3,0.42],[2,0.42],[-4,1,5]],{name:'b',snapWidth:0.1});
var intex1_i1S = intex1_board5.create('integral', [[function(){return pinfC.Value()},function(){return psupC.Value()} ], intex1_c1],{withLabel: false,fixed:true,fillColor:'blue'}); 
intex1_i1S.curveLeft.setProperty({visible:false}); 
intex1_i1S.curveRight.setProperty({visible:false});
for(var i=-4;i<4;i=i+0.5){
  intex1_board5.create('segment',[ [i,-0.01] , [i,0.01] ],{strokeColor:'black',fixed:true,strokeWidth:1});
  intex1_board5.create('text',[i-0.2,-0.02,i],{fixed:true});
}
intex1_board5.create('text',[-4,0.35,function(){var p = Math.floor( intex1_i1S.Value()*1000000 )/1000000;return '
P( a < X < b )='+Math.round(100000*p)/100000+'
';}],{fixed:true,strokeColor:'blue'});
var t1 = intex1_board5.create('text',[function(){return (pinfC.X()+psupC.X())/2-0.5;},0.2,'
P(a< X < b)
'],{fixed:true});
</script>

<div id="ed4BboxFtyy" class='jxgbox' style="margin:auto;width: 350px; height: 350px;margin-top:20px;margin-bottom:15px;"></div> 
<script type="text/javascript"> 
var intex1_board35 = JXG.JSXGraph.initBoard('ed4BboxFtyy', {boundingbox: [-10, 0.8, 10, -0.05], showcopyright: false, axes:true, shownavigation: false,grid:false,pan:{enabled:false}}); 
var absAxe = intex1_board35.create('arrow',[ [-10,0.00],[10,0.00] ], {strokeColor: 'black', strokeWidth:2,fixed:true}); 
var absOrd = intex1_board35.create('arrow',[ [0,-1],[0,0.8] ], {strokeColor: 'black',fixed:true}); 
var mu = intex1_board35.create('slider',[[-9.5,0.67],[6,0.67],[-5,1,5]],{name:'μ',snapWidth:0.01});
var sigma = intex1_board35.create('slider',[[-9.5,0.62],[6,0.62],[0.1,1,5]],{name:'σ',snapWidth:0.01});
var intex1_c1 = intex1_board35.create('functiongraph', [function (x) { return  0.3989422804*Math.pow( 2.718281828,(-0.5*( x-mu.Value() )*( x-mu.Value() )/(sigma.Value()*sigma.Value() ) ) )/sigma.Value(); }],{strokeWidth:2}); 
for(var i=-9;i<10;i=i+1){
  intex1_board35.create('segment',[ [i,-0.01] , [i,0.01] ],{strokeColor:'black',fixed:true,strokeWidth:1});
  intex1_board35.create('text',[i-0.2,-0.03,i],{fixed:true});
}
</script>

<div id="d4boxFtyyXF" class='jxgbox' style="margin:auto;width: 350px; height: 350px;margin-top:20px;margin-bottom:15px;"></div> 
<script type="text/javascript"> 
var intex1_board3 = JXG.JSXGraph.initBoard('d4boxFtyyXF', {boundingbox: [-4, 0.5, 4, -0.05], showcopyright: false, axes:true, shownavigation: false,grid:false,pan:{enabled:false}}); 
var absAxe = intex1_board3.create('arrow',[ [-5,0.00],[4,0.00] ], {strokeColor: 'black', strokeWidth:2,fixed:true}); 
var absOrd = intex1_board3.create('arrow',[ [0,-1],[0,0.5] ], {strokeColor: 'black',fixed:true}); 
var intex1_c1 = intex1_board3.create('functiongraph', [function (x) { return  0.3989422804*Math.pow( 2.718281828,(-0.5*x*x) ); }]); 
var intex1_i1 = intex1_board3.create('integral', [[-1.2,1.2], intex1_c1],{withLabel: false,fixed:true,fillColor:'blue'}); 
intex1_i1.curveLeft.setProperty({visible:false}); 
intex1_i1.curveRight.setProperty({visible:false});
var t1 = intex1_board3.create('point',[-1.2,0],{name:function(){return '-u_{α}'},fixed:true,strokeColor:'black',fillColor:'black',label:{offset:[-5,-15]}});
var t2 = intex1_board3.create('point',[1.2,0],{name:function(){return '+u_{α}'},fixed:true,strokeColor:'black',fillColor:'black',label:{offset:[-5,-15]}});
var t3 = intex1_board3.create('text',[-3.8,0.2,'P( X < -u_{α} ) = α/2'],{fixed:true,strokeColor:'black'});
var t4 = intex1_board3.create('text',[1.7,0.2,'P( X > u_{α} ) = α/2'],{fixed:true,strokeColor:'black'});
var s1 = intex1_board3.create('arrow',[ [-2.8,0.18],[-1.5,0.05] ],{dash:1,strokeColor:'black',strokeWidth:1.5,fixed:true});
var s2 = intex1_board3.create('arrow',[ [2.8,0.18],[1.5,0.05] ],{dash:1,strokeColor:'black',strokeWidth:1.5,fixed:true});
var t5 = intex1_board3.create('text',[-1.2,0.45,'
P(u_{α} ≤  X ≤ u_{α} ) = 1 - α
'],{fixed:true,strokeColor:'black'});
var s3 = intex1_board3.create('arrow',[ [-0.6,0.43],[-0.2,0.3] ],{dash:1,strokeColor:'black',strokeWidth:1.5,fixed:true});
</script>

<div id='bbProbas' class='jxgbox' style='width:350px; height:350px;margin:auto;margin-top:20px;margin-bottom:40px;'></div> 
<script> 
var board = JXG.JSXGraph.initBoard('bbProbas', {boundingbox: [-12, 10, 8, -10], showCopyright:false,showNavigation:false,pan:{enabled:false}}); 
var s1 = board.create('segment',[[-9,0],[-4,4]],{fixed:true});
var s2 = board.create('segment',[[-9,0],[-4,-4]],{fixed:true});
var s3 = board.create('segment',[[-3,4.5],[2,8]],{fixed:true});
var s4 = board.create('segment',[[-3,3.5],[2,1]],{fixed:true});
var s5 = board.create('segment',[[-3,-4.5],[2,-8]],{fixed:true});
var s6 = board.create('segment',[[-3,-3.5],[2,-1]],{fixed:true});
var t1 = board.create('text',[-3.7,4.2,'R'],{fixed:true});
var t2 = board.create('text',[-3.7,-3.8,'R'],{fixed:true});
var t21 = board.create('text',[-3.7,-3.4,'–'],{fixed:true});
var t3 = board.create('text',[2.3, 8.2,'J'],{fixed:true});
var t4 = board.create('text',[2.3, 1.2,'J'],{fixed:true});
var t41 = board.create('text',[2.3,1.6,'–'],{fixed:true});
var t5 = board.create('text',[2.3, -7.8,'J'],{fixed:true});
var t51 = board.create('text',[2.3,-7.4,'–'],{fixed:true});
var t6 = board.create('text',[2.3, -0.8,'J'],{fixed:true});
var p1 = board.create('text',[-7, 3.1,'0,4'],{fixed:true,strokeColor:'red'});
var p2 = board.create('text',[-7, -2.8,'0,6'],{fixed:true,strokeColor:'red'});
var p3 = board.create('text',[-1, 7.6,'0,25'],{fixed:true,strokeColor:'red'});
var p4 = board.create('text',[-1, 1.8,'0,75'],{fixed:true,strokeColor:'red'});
var p5 = board.create('text',[-1, -1.5,'x'],{fixed:true,strokeColor:'red'});
var p6 = board.create('text',[-1, -6.5,'1-x'],{fixed:true,strokeColor:'red'});
</script>